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<p>This header is part of the <a href="../numeric.html" title="cpp/numeric">numeric</a> library.
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<table id="toc" class="toc"><tr><td><div id="toctitle"><h2>Contents</h2></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="complex.html#Classes"><span class="tocnumber">1</span> <span class="toctext">Classes</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="complex.html#Functions"><span class="tocnumber">2</span> <span class="toctext">Functions</span></a>
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<li class="toclevel-2"><a href="complex.html#Operations"><span class="tocnumber">2.1</span> <span class="toctext">Operations</span></a></li>
<li class="toclevel-2"><a href="complex.html#Exponential_functions"><span class="tocnumber">2.2</span> <span class="toctext">Exponential functions</span></a></li>
<li class="toclevel-2"><a href="complex.html#Power_functions"><span class="tocnumber">2.3</span> <span class="toctext">Power functions</span></a></li>
<li class="toclevel-2"><a href="complex.html#Trigonometric_functions"><span class="tocnumber">2.4</span> <span class="toctext">Trigonometric functions</span></a></li>
<li class="toclevel-2"><a href="complex.html#Hyperbolic_functions"><span class="tocnumber">2.5</span> <span class="toctext">Hyperbolic functions</span></a></li>
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<li class="toclevel-1 tocsection-3"><a href="complex.html#Synopsis"><span class="tocnumber">3</span> <span class="toctext">Synopsis</span></a>
<ul>
<li class="toclevel-2 tocsection-4"><a href="complex.html#Class_std::complex"><span class="tocnumber">3.1</span> <span class="toctext">Class <span>std::complex</span></span></a></li>
<li class="toclevel-2 tocsection-5"><a href="complex.html#std::complex_specializations"><span class="tocnumber">3.2</span> <span class="toctext"><span>std::complex</span> specializations</span></a></li>
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<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=cpp/header/complex&action=edit&section=1" title="Edit section: Classes">edit</a>]</span> <span class="mw-headline" id="Classes">Classes</span></h3>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex.html" title="cpp/numeric/complex"> <span class="t-lines"><span>complex</span></span></a></div></div>
</td>
<td> a complex number type <br /> <span class="t-mark">(class template)</span>
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<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex.html" title="cpp/numeric/complex"> <span class="t-lines"><span><code><b>complex</b></code><span style="font-size:0.7em; line-height:130%"><float></span></span><span><code><b>complex</b></code><span style="font-size:0.7em; line-height:130%"><double></span></span><span><code><b>complex</b></code><span style="font-size:0.7em; line-height:130%"><long double></span></span></span></a></div></div>
</td>
<td> a complex number type <br /> <span class="t-mark">(class template specialization)</span>
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<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=cpp/header/complex&action=edit&section=2" title="Edit section: Functions">edit</a>]</span> <span class="mw-headline" id="Functions">Functions</span></h3>
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<td colspan="2"> <h5> <span class="mw-headline" id="Operations"> Operations </span></h5>
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<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/operator_arith2.html" title="cpp/numeric/complex/operator arith2"> <span class="t-lines"><span>operator+</span><span>operator-</span></span></a></div></div>
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<td> applies unary operators to complex numbers <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_operator_arith2&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/operator_arith3.html" title="cpp/numeric/complex/operator arith3"> <span class="t-lines"><span>operator+</span><span>operator-</span><span>operator*</span><span>operator/</span></span></a></div></div>
</td>
<td> performs complex number arithmetics on two complex values or a complex and a scalar <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_operator_arith3&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/operator_cmp.html" title="cpp/numeric/complex/operator cmp"> <span class="t-lines"><span>operator==</span><span>operator!=</span></span></a></div></div>
</td>
<td> compares two complex numbers or a complex and a scalar <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_operator_cmp&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/operator_ltltgtgt.html" title="cpp/numeric/complex/operator ltltgtgt"> <span class="t-lines"><span>operator<<</span><span>operator>></span></span></a></div></div>
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<td> serializes and deserializes a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_operator_ltltgtgt&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/real2.html" title="cpp/numeric/complex/real2"> <span class="t-lines"><span>real</span></span></a></div></div>
</td>
<td> returns the real component <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_real2&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/imag2.html" title="cpp/numeric/complex/imag2"> <span class="t-lines"><span>imag</span></span></a></div></div>
</td>
<td> returns the imaginary component <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_imag2&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/abs.html" title="cpp/numeric/complex/abs"> <span class="t-lines"><span>abs<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> returns the magnitude of a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_abs&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/arg.html" title="cpp/numeric/complex/arg"> <span class="t-lines"><span>arg</span></span></a></div></div>
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<td> returns the phase angle <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_arg&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/norm.html" title="cpp/numeric/complex/norm"> <span class="t-lines"><span>norm</span></span></a></div></div>
</td>
<td> returns the squared magnitude <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_norm&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/conj.html" title="cpp/numeric/complex/conj"> <span class="t-lines"><span>conj</span></span></a></div></div>
</td>
<td> returns the complex conjugate <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_conj&action=edit">[edit]</a></span>
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<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/proj.html" title="cpp/numeric/complex/proj"> <span class="t-lines"><span>proj</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> returns the projection onto the Riemann sphere <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_proj&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/polar.html" title="cpp/numeric/complex/polar"> <span class="t-lines"><span>polar</span></span></a></div></div>
</td>
<td> constructs a complex number from magnitude and phase angle <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_polar&action=edit">[edit]</a></span>
</td></tr>
<tr>
<td colspan="2"> <h5> <span class="mw-headline" id="Exponential_functions"> Exponential functions </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/exp.html" title="cpp/numeric/complex/exp"> <span class="t-lines"><span>exp<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> complex base <i>e</i> exponential <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_exp&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/log.html" title="cpp/numeric/complex/log"> <span class="t-lines"><span>log<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> complex natural logarithm with the branch cuts along the negative real axis <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_log&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/log10.html" title="cpp/numeric/complex/log10"> <span class="t-lines"><span>log10<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> complex common logarithm with the branch cuts along the negative real axis <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_log10&action=edit">[edit]</a></span>
</td></tr>
<tr>
<td colspan="2"> <h5> <span class="mw-headline" id="Power_functions"> Power functions </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/pow.html" title="cpp/numeric/complex/pow"> <span class="t-lines"><span>pow<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> complex power, one or both arguments may be a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_pow&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/sqrt.html" title="cpp/numeric/complex/sqrt"> <span class="t-lines"><span>sqrt<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> complex square root in the range of the right half-plane <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_sqrt&action=edit">[edit]</a></span>
</td></tr>
<tr>
<td colspan="2"> <h5> <span class="mw-headline" id="Trigonometric_functions"> Trigonometric functions </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/sin.html" title="cpp/numeric/complex/sin"> <span class="t-lines"><span>sin<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> computes sine of a complex number (<span class="texhtml" style="white-space: nowrap;">sin(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_sin&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/cos.html" title="cpp/numeric/complex/cos"> <span class="t-lines"><span>cos<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> computes cosine of a complex number (<span class="texhtml" style="white-space: nowrap;">cos(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_cos&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/tan.html" title="cpp/numeric/complex/tan"> <span class="t-lines"><span>tan<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> computes tangent of a complex number (<span class="texhtml" style="white-space: nowrap;">tan(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_tan&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/asin.html" title="cpp/numeric/complex/asin"> <span class="t-lines"><span>asin<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> computes arc sine of a complex number (<span class="texhtml" style="white-space: nowrap;">arcsin(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_asin&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/acos.html" title="cpp/numeric/complex/acos"> <span class="t-lines"><span>acos<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> computes arc cosine of a complex number (<span class="texhtml" style="white-space: nowrap;">arccos(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_acos&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/atan.html" title="cpp/numeric/complex/atan"> <span class="t-lines"><span>atan<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> computes arc tangent of a complex number (<span class="texhtml" style="white-space: nowrap;">arctan(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_atan&action=edit">[edit]</a></span>
</td></tr>
<tr>
<td colspan="2"> <h5> <span class="mw-headline" id="Hyperbolic_functions"> Hyperbolic functions </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/sinh.html" title="cpp/numeric/complex/sinh"> <span class="t-lines"><span>sinh<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> computes hyperbolic sine of a complex number (<span class="texhtml" style="white-space: nowrap;">sh(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_sinh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/cosh.html" title="cpp/numeric/complex/cosh"> <span class="t-lines"><span>cosh<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> computes hyperbolic cosine of a complex number (<span class="texhtml" style="white-space: nowrap;">ch(z)</span>) <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_cosh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/tanh.html" title="cpp/numeric/complex/tanh"> <span class="t-lines"><span>tanh<span class="t-dsc-small">(std::complex)</span></span></span></a></div></div>
</td>
<td> computes hyperbolic tangent of a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_tanh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/asinh.html" title="cpp/numeric/complex/asinh"> <span class="t-lines"><span>asinh<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> computes area hyperbolic sine of a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_asinh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/acosh.html" title="cpp/numeric/complex/acosh"> <span class="t-lines"><span>acosh<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> computes area hyperbolic cosine of a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_acosh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="../numeric/complex/atanh.html" title="cpp/numeric/complex/atanh"> <span class="t-lines"><span>atanh<span class="t-dsc-small">(std::complex)</span></span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div>
</td>
<td> computes area hyperbolic tangent of a complex number <br /> <span class="t-mark">(function template)</span> <span class="editsection noprint plainlinks" title="Edit this template"><a rel="nofollow" class="external text" href="http://en.cppreference.com/mwiki/index.php?title=Template:cpp/numeric/complex/dsc_atanh&action=edit">[edit]</a></span>
</td></tr>
</table>
<p><br />
</p>
<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=cpp/header/complex&action=edit&section=3" title="Edit section: Synopsis">edit</a>]</span> <span class="mw-headline" id="Synopsis">Synopsis</span></h3>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="cpp source-cpp"><pre class="de1"><span class="kw1">namespace</span> std <span class="br0">{</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw1">class</span> complex<span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><></span> <span class="kw1">class</span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><></span> <span class="kw1">class</span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><></span> <span class="kw1">class</span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy4">;</span>
 
<span class="co1">// operators:</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span>
complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">+</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">+</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">+</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">-</span><span class="br0">(</span>
<span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">-</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">-</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">*</span><span class="br0">(</span>
<span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">*</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">*</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">/</span><span class="br0">(</span>
<span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">/</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">/</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">+</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> operator<span class="sy2">-</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw4">bool</span> operator<span class="sy1">==</span><span class="br0">(</span>
<span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw4">bool</span> operator<span class="sy1">==</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw4">bool</span> operator<span class="sy1">==</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw4">bool</span> operator<span class="sy3">!</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw4">bool</span> operator<span class="sy3">!</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> <span class="kw4">bool</span> operator<span class="sy3">!</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T, <span class="kw1">class</span> charT, <span class="kw1">class</span> traits<span class="sy1">></span>
basic_istream<span class="sy1"><</span>charT, traits<span class="sy1">></span><span class="sy3">&</span>
operator<span class="sy1">>></span><span class="br0">(</span>basic_istream<span class="sy1"><</span>charT, traits<span class="sy1">></span><span class="sy3">&</span>, complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T, <span class="kw1">class</span> charT, <span class="kw1">class</span> traits<span class="sy1">></span>
basic_ostream<span class="sy1"><</span>charT, traits<span class="sy1">></span><span class="sy3">&</span>
operator<span class="sy1"><<</span><span class="br0">(</span>basic_ostream<span class="sy1"><</span>charT, traits<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="co1">// values:</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> T real<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> T imag<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> T abs<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> T arg<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> T norm<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> conj<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span> <span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> proj<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> polar<span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span> <span class="sy1">=</span> <span class="nu0">0</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="co1">// transcendentals:</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> acos<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> asin<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> atan<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> acosh<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> asinh<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> atanh<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> cos <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> cosh <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> exp <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> log <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> log10<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> pow<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> pow<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> pow<span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span>, <span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> sin <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> sinh <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> sqrt <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> tan <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span> tanh <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
 
<span class="br0">}</span></pre></div></div>
<p><br />
</p>
<h4><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=cpp/header/complex&action=edit&section=4" title="Edit section: Class std::complex">edit</a>]</span> <span class="mw-headline" id="Class_std::complex">Class <span class="t-lc"><a href="../numeric/complex.html" title="cpp/numeric/complex">std::complex</a></span></span></h4>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="cpp source-cpp"><pre class="de1"><span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> T<span class="sy1">></span>
<span class="kw1">class</span> complex <span class="br0">{</span>
<span class="kw1">public</span><span class="sy4">:</span>
<span class="kw1">typedef</span> T value_type<span class="sy4">;</span>
complex<span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span> re <span class="sy1">=</span> T<span class="br0">(</span><span class="br0">)</span>, <span class="kw4">const</span> T<span class="sy3">&</span> im <span class="sy1">=</span> T<span class="br0">(</span><span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
T real<span class="br0">(</span><span class="br0">)</span> <span class="kw4">const</span><span class="sy4">;</span>
<span class="kw4">void</span> real<span class="br0">(</span>T<span class="br0">)</span><span class="sy4">;</span>
T imag<span class="br0">(</span><span class="br0">)</span> <span class="kw4">const</span><span class="sy4">;</span>
<span class="kw4">void</span> imag<span class="br0">(</span>T<span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> T<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy3">&</span> operator<span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span>T<span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="br0">}</span><span class="sy4">;</span></pre></div></div>
<h4><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=cpp/header/complex&action=edit&section=5" title="Edit section: std::complex specializations">edit</a>]</span> <span class="mw-headline" id="std::complex_specializations"><span class="t-lc"><a href="../numeric/complex.html" title="cpp/numeric/complex">std::complex</a></span> specializations</span></h4>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="cpp source-cpp"><pre class="de1"><span class="kw1">template</span><span class="sy1"><></span> <span class="kw1">class</span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span> <span class="br0">{</span>
<span class="kw1">public</span><span class="sy4">:</span>
<span class="kw1">typedef</span> <span class="kw4">float</span> value_type<span class="sy4">;</span>
 
<span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">float</span> re <span class="sy1">=</span> <span class="nu17">0.0f</span>, <span class="kw4">float</span> im <span class="sy1">=</span> <span class="nu17">0.0f</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">explicit</span> <span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">explicit</span> <span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw4">constexpr</span> <span class="kw4">float</span> real<span class="br0">(</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">void</span> real<span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">constexpr</span> <span class="kw4">float</span> imag<span class="br0">(</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">void</span> imag<span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">float</span><span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><></span> <span class="kw1">class</span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span> <span class="br0">{</span>
<span class="kw1">public</span><span class="sy4">:</span>
<span class="kw1">typedef</span> <span class="kw4">double</span> value_type<span class="sy4">;</span>
 
<span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">double</span> re <span class="sy1">=</span> <span class="nu16">0.0</span>, <span class="kw4">double</span> im <span class="sy1">=</span> <span class="nu16">0.0</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">explicit</span> <span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw4">constexpr</span> <span class="kw4">double</span> real<span class="br0">(</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">void</span> real<span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">constexpr</span> <span class="kw4">double</span> imag<span class="br0">(</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">void</span> imag<span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><></span> <span class="kw1">class</span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span> <span class="br0">{</span>
<span class="kw1">public</span><span class="sy4">:</span>
<span class="kw1">typedef</span> <span class="kw4">long</span> <span class="kw4">double</span> value_type<span class="sy4">;</span>
 
<span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span> re <span class="sy1">=</span> 0.0L, <span class="kw4">long</span> <span class="kw4">double</span> im <span class="sy1">=</span> 0.0L<span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">float</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">constexpr</span> complex<span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw4">constexpr</span> <span class="kw4">long</span> <span class="kw4">double</span> real<span class="br0">(</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">void</span> real<span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">constexpr</span> <span class="kw4">long</span> <span class="kw4">double</span> imag<span class="br0">(</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">void</span> imag<span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
 
complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">long</span> <span class="kw4">double</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy1">=</span> <span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">+</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">-</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">*</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw1">template</span><span class="sy1"><</span><span class="kw1">class</span> X<span class="sy1">></span> complex<span class="sy1"><</span><span class="kw4">long</span> <span class="kw4">double</span><span class="sy1">></span><span class="sy3">&</span> operator<span class="sy2">/</span><span class="sy1">=</span><span class="br0">(</span><span class="kw4">const</span> complex<span class="sy1"><</span>X<span class="sy1">></span><span class="sy3">&</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="br0">}</span><span class="sy4">;</span></pre></div></div>
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