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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/complex.html" title="c/numeric/complex/complex"><span class="t-lines"><span>complex</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/Complex_I.html" title="c/numeric/complex/Complex I"><span class="t-lines"><span>_Complex_I</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/CMPLX.html" title="c/numeric/complex/CMPLX"><span class="t-lines"><span>CMPLX</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/imaginary.html" title="c/numeric/complex/imaginary"><span class="t-lines"><span>imaginary</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/Imaginary_I.html" title="c/numeric/complex/Imaginary I"><span class="t-lines"><span>_Imaginary_I</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/I.html" title="c/numeric/complex/I"><span class="t-lines"><span>I</span></span></a></div></div></td></tr>
</table></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> Manipulation</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cimag.html" title="c/numeric/complex/cimag"><span class="t-lines"><span>cimag</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/creal.html" title="c/numeric/complex/creal"><span class="t-lines"><span>creal</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/carg.html" title="c/numeric/complex/carg"><span class="t-lines"><span>carg</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cabs.html" title="c/numeric/complex/cabs"><span class="t-lines"><span>cabs</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/conj.html" title="c/numeric/complex/conj"><span class="t-lines"><span>conj</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cproj.html" title="c/numeric/complex/cproj"><span class="t-lines"><span>cproj</span></span></a></div></div></td></tr>
</table></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> Power and exponential functions</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cexp.html" title="c/numeric/complex/cexp"><span class="t-lines"><span>cexp</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/clog.html" title="c/numeric/complex/clog"><span class="t-lines"><span>clog</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cpow.html" title="c/numeric/complex/cpow"><span class="t-lines"><span>cpow</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/csqrt.html" title="c/numeric/complex/csqrt"><span class="t-lines"><span>csqrt</span></span></a></div></div></td></tr>
</table></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> Trigonometric functions</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/ccos.html" title="c/numeric/complex/ccos"><span class="t-lines"><span>ccos</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/csin.html" title="c/numeric/complex/csin"><span class="t-lines"><span>csin</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/ctan.html" title="c/numeric/complex/ctan"><span class="t-lines"><span>ctan</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cacos.html" title="c/numeric/complex/cacos"><span class="t-lines"><span>cacos</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/casin.html" title="c/numeric/complex/casin"><span class="t-lines"><span>casin</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/catan.html" title="c/numeric/complex/catan"><span class="t-lines"><span>catan</span></span></a></div></div></td></tr>
</table></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> Hyperbolic functions</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/ccosh.html" title="c/numeric/complex/ccosh"><span class="t-lines"><span>ccosh</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/csinh.html" title="c/numeric/complex/csinh"><span class="t-lines"><span>csinh</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/ctanh.html" title="c/numeric/complex/ctanh"><span class="t-lines"><span>ctanh</span></span></a></div></div></td></tr>
</table></div></td><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/cacosh.html" title="c/numeric/complex/cacosh"><span class="t-lines"><span>cacosh</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/casinh.html" title="c/numeric/complex/casinh"><span class="t-lines"><span>casinh</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="complex/catanh.html" title="c/numeric/complex/catanh"><span class="t-lines"><span>catanh</span></span></a></div></div></td></tr>
</table></div></td></tr>
</table></div><div><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:c/numeric/complex/navbar_content&action=edit">[edit]</a></span></div></div></div></div><div class="t-navbar-sep"> </div></div>
<table class="t-rev-begin">
<tr class="t-rev t-since-c11"><td>
If the macro constant <code>__STDC_NO_COMPLEX__</code> is defined by the implementation, the complex types, the header <code><complex.h></code> and all of the names listed here are not provided.</td>
<td><span class="t-mark-rev t-since-c11">(since C11)</span></td></tr>
</table>
<p>The C programming language, as of C99, supports complex number math with the three built-in types <code>double _Complex</code>, <code>float _Complex</code>, and <code>long double _Complex</code> (see <a href="../keyword/_Complex.html" title="c/keyword/ Complex">_Complex</a>). When the header <code><complex.h></code> is included, the three complex number types are also accessible as <code>double complex</code>, <code>float complex</code>, <code>long double complex</code>.
</p><p>In addition to the complex types, the three imaginary types may be supported: <code>double _Imaginary</code>, <code>float _Imaginary</code>, and <code>long double _Imaginary</code> (see <a href="../keyword/_Imaginary.html" title="c/keyword/ Imaginary">_Imaginary</a>). When the header <code><complex.h></code> is included, the three imaginary types are also accessible as <code>double imaginary</code>, <code>float imaginary</code>, and <code>long double imaginary</code>.
</p><p>Standard arithmetic operators <span class="t-c"><span class="mw-geshi c source-c"><span class="sy2">+</span>, <span class="sy2">-</span>, <span class="sy2">*</span>, <span class="sy2">/</span></span></span> can be used with real, complex, and imaginary types in any combination.
</p>
<table class="t-rev-begin">
<tr class="t-rev t-since-c99 t-until-c11"><td>
<p>A compiler that defines <span class="t-c"><span class="mw-geshi c source-c">__STDC_IEC_559_COMPLEX__</span></span> is recommended, but not required to support imaginary numbers. POSIX recommends checking if the macro <span class="t-c"><span class="mw-geshi c source-c"><a href="complex/Imaginary_I.html"><span class="kw746">_Imaginary_I</span></a></span></span> is defined to identify imaginary number support.
</p>
</td>
<td><span class="t-mark-rev t-since-c99">(since C99)</span><br /><span class="t-mark-rev t-until-c11">(until C11)</span></td></tr>
<tr class="t-rev t-since-c11"><td>
<p>Imaginary numbers are supported if <span class="t-c"><span class="mw-geshi c source-c">__STDC_IEC_559_COMPLEX__</span></span> is defined.
</p>
</td>
<td><span class="t-mark-rev t-since-c11">(since C11)</span></td></tr>
</table>
<table class="t-dsc-begin">
<tr class="t-dsc-header">
<td colspan="2"> <div>Defined in header <code><complex.h></code> </div>
</td></tr>
<tr>
<td colspan="2"> <table id="toc" class="toc"><tr><td><div id="toctitle"><h2>Contents</h2></div>
<ul>
<li class="toclevel-1"><a href="complex.html#Types"><span class="tocnumber">1</span> <span class="toctext">Types</span></a></li>
<li class="toclevel-1"><a href="complex.html#The_imaginary_constant"><span class="tocnumber">2</span> <span class="toctext">The imaginary constant</span></a></li>
<li class="toclevel-1"><a href="complex.html#Manipulation"><span class="tocnumber">3</span> <span class="toctext">Manipulation</span></a></li>
<li class="toclevel-1"><a href="complex.html#Exponential_functions"><span class="tocnumber">4</span> <span class="toctext">Exponential functions</span></a></li>
<li class="toclevel-1"><a href="complex.html#Power_functions"><span class="tocnumber">5</span> <span class="toctext">Power functions</span></a></li>
<li class="toclevel-1"><a href="complex.html#Trigonometric_functions"><span class="tocnumber">6</span> <span class="toctext">Trigonometric functions</span></a></li>
<li class="toclevel-1"><a href="complex.html#Hyperbolic_functions"><span class="tocnumber">7</span> <span class="toctext">Hyperbolic functions</span></a></li>
<li class="toclevel-1 tocsection-1"><a href="complex.html#Notes"><span class="tocnumber">8</span> <span class="toctext">Notes</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="complex.html#Example"><span class="tocnumber">9</span> <span class="toctext">Example</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="complex.html#References"><span class="tocnumber">10</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-4"><a href="complex.html#See_also"><span class="tocnumber">11</span> <span class="toctext">See also</span></a></li>
</ul>
</td></tr></table>
<h5> <span class="mw-headline" id="Types"> Types </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/imaginary.html" title="c/numeric/complex/imaginary"> <span class="t-lines"><span>imaginary</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> imaginary type macro <br /> <span class="t-mark">(macro constant)</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:c/numeric/complex/dsc_imaginary&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/complex.html" title="c/numeric/complex/complex"> <span class="t-lines"><span>complex</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> complex type macro <br /> <span class="t-mark">(macro constant)</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:c/numeric/complex/dsc_complex&action=edit">[edit]</a></span>
</td></tr>
<tr>
<td colspan="2"> <h5> <span class="mw-headline" id="The_imaginary_constant"> The imaginary constant </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/Imaginary_I.html" title="c/numeric/complex/Imaginary I"> <span class="t-lines"><span>_Imaginary_I</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> the imaginary unit constant i <br /> <span class="t-mark">(macro constant)</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:c/numeric/complex/dsc_Imaginary_I&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/Complex_I.html" title="c/numeric/complex/Complex I"> <span class="t-lines"><span>_Complex_I</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> the complex unit constant i <br /> <span class="t-mark">(macro constant)</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:c/numeric/complex/dsc_Complex_I&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/I.html" title="c/numeric/complex/I"> <span class="t-lines"><span>I</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> the complex or imaginary unit constant i <br /> <span class="t-mark">(macro constant)</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:c/numeric/complex/dsc_I&action=edit">[edit]</a></span>
</td></tr>
<tr>
<td colspan="2"> <h5> <span class="mw-headline" id="Manipulation"> Manipulation </span></h5>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/CMPLX.html" title="c/numeric/complex/CMPLX"> <span class="t-lines"><span>CMPLX</span><span>CMPLXF</span><span>CMPLXL</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c11">(C11)</span></span><span><span class="t-mark-rev t-since-c11">(C11)</span></span><span><span class="t-mark-rev t-since-c11">(C11)</span></span></span></div></div>
</td>
<td> constructs a complex number from real and imaginary parts <br /> <span class="t-mark">(function macro)</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:c/numeric/complex/dsc_CMPLX&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/creal.html" title="c/numeric/complex/creal"> <span class="t-lines"><span>creal</span><span>crealf</span><span>creall</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the real part of a complex number <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_creal&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/cimag.html" title="c/numeric/complex/cimag"> <span class="t-lines"><span>cimag</span><span>cimagf</span><span>cimagl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the imaginary part a complex number <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cimag&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/cabs.html" title="c/numeric/complex/cabs"> <span class="t-lines"><span>cabs</span><span>cabsf</span><span>cabsl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the magnitude of a complex number <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cabs&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/carg.html" title="c/numeric/complex/carg"> <span class="t-lines"><span>carg</span><span>cargf</span><span>cargl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the phase angle of a complex number <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_carg&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/conj.html" title="c/numeric/complex/conj"> <span class="t-lines"><span>conj</span><span>conjf</span><span>conjl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex conjugate <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_conj&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/cproj.html" title="c/numeric/complex/cproj"> <span class="t-lines"><span>cproj</span><span>cprojf</span><span>cprojl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the projection on Riemann sphere <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cproj&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="complex/cexp.html" title="c/numeric/complex/cexp"> <span class="t-lines"><span>cexp</span><span>cexpf</span><span>cexpl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex base-e exponential <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cexp&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/clog.html" title="c/numeric/complex/clog"> <span class="t-lines"><span>clog</span><span>clogf</span><span>clogl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex natural logarithm <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_clog&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="complex/cpow.html" title="c/numeric/complex/cpow"> <span class="t-lines"><span>cpow</span><span>cpowf</span><span>cpowl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex power function <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cpow&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/csqrt.html" title="c/numeric/complex/csqrt"> <span class="t-lines"><span>csqrt</span><span>csqrtf</span><span>csqrtl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex square root <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_csqrt&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="complex/csin.html" title="c/numeric/complex/csin"> <span class="t-lines"><span>csin</span><span>csinf</span><span>csinl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex sine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_csin&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/ccos.html" title="c/numeric/complex/ccos"> <span class="t-lines"><span>ccos</span><span>ccosf</span><span>ccosl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex cosine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_ccos&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/ctan.html" title="c/numeric/complex/ctan"> <span class="t-lines"><span>ctan</span><span>ctanf</span><span>ctanl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex tangent <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_ctan&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/casin.html" title="c/numeric/complex/casin"> <span class="t-lines"><span>casin</span><span>casinf</span><span>casinl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex arc sine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_casin&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/cacos.html" title="c/numeric/complex/cacos"> <span class="t-lines"><span>cacos</span><span>cacosf</span><span>cacosl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex arc cosine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cacos&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/catan.html" title="c/numeric/complex/catan"> <span class="t-lines"><span>catan</span><span>catanf</span><span>catanl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex arc tangent <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_catan&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="complex/csinh.html" title="c/numeric/complex/csinh"> <span class="t-lines"><span>csinh</span><span>csinhf</span><span>csinhl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex hyperbolic sine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_csinh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/ccosh.html" title="c/numeric/complex/ccosh"> <span class="t-lines"><span>ccosh</span><span>ccoshf</span><span>ccoshl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex hyperbolic cosine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_ccosh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/ctanh.html" title="c/numeric/complex/ctanh"> <span class="t-lines"><span>ctanh</span><span>ctanhf</span><span>ctanhl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex hyperbolic tangent <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_ctanh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/casinh.html" title="c/numeric/complex/casinh"> <span class="t-lines"><span>casinh</span><span>casinhf</span><span>casinhl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex arc hyperbolic sine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_casinh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/cacosh.html" title="c/numeric/complex/cacosh"> <span class="t-lines"><span>cacosh</span><span>cacoshf</span><span>cacoshl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex arc hyperbolic cosine <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_cacosh&action=edit">[edit]</a></span>
</td></tr>
<tr class="t-dsc">
<td> <div class="t-dsc-member-div"><div><a href="complex/catanh.html" title="c/numeric/complex/catanh"> <span class="t-lines"><span>catanh</span><span>catanhf</span><span>catanhl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td> computes the complex arc hyperbolic tangent <br /> <span class="t-mark">(function)</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:c/numeric/complex/dsc_catanh&action=edit">[edit]</a></span>
</td></tr>
</table>
<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=c/numeric/complex&action=edit&section=1" title="Edit section: Notes">edit</a>]</span> <span class="mw-headline" id="Notes">Notes</span></h3>
<p>The following function names are reserved for future addition to <code>complex.h</code> and are not available for use in the programs that include that header: <code>cerf</code>, <code>cerfc</code>, <code>cexp2</code>, <code>cexpm1</code>, <code>clog10</code>, <code>clog1p</code>, <code>clog2</code>, <code>clgamma</code>, and <code>ctgamma</code>, along with their -f and -l suffixed variants.
</p><p>Although the C standard names the inverse hyperbolics with "complex arc hyperbolic sine" etc., the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct names are "complex inverse hyperbolic sine" etc. Some authors use "complex area hyperbolic sine" etc.
</p><p>A complex or imaginary number is infinite if one of its components is infinite, even if the other component is NaN.
</p><p>A complex or imaginary number is finite if both components are neither infinities nor NaNs.
</p><p>A complex or imaginary number is a zero if both components are positive or negative zeroes.
</p>
<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=c/numeric/complex&action=edit&section=2" title="Edit section: Example">edit</a>]</span> <span class="mw-headline" id="Example">Example</span></h3>
<div class="t-example"><div class="t-example-live-link"><div class="coliru-btn coliru-btn-run-init">Run this code</div></div>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="c source-c"><pre class="de1"><span class="co2">#include <stdio.h></span>
<span class="co2">#include <complex.h></span>
<span class="co2">#include <tgmath.h></span>
 
<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
<span class="br0">{</span>
<span class="kw4">double</span> <a href="complex/complex.html"><span class="kw743">complex</span></a> z1 <span class="sy1">=</span> I <span class="sy2">*</span> I<span class="sy4">;</span> <span class="co1">// imaginary unit squared</span>
<a href="../io/fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"I * I = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="complex/creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z1<span class="br0">)</span>, <a href="complex/cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z1<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw4">double</span> <a href="complex/complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> <a href="math/pow.html"><span class="kw668">pow</span></a><span class="br0">(</span>I, <span class="nu0">2</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// imaginary unit squared</span>
<a href="../io/fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"pow(I, 2) = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="complex/creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z2<span class="br0">)</span>, <a href="complex/cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z2<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw4">double</span> PI <span class="sy1">=</span> <a href="math/acos.html"><span class="kw673">acos</span></a><span class="br0">(</span><span class="sy2">-</span><span class="nu0">1</span><span class="br0">)</span><span class="sy4">;</span>
<span class="kw4">double</span> <a href="complex/complex.html"><span class="kw743">complex</span></a> z3 <span class="sy1">=</span> <a href="math/exp.html"><span class="kw657">exp</span></a><span class="br0">(</span>I <span class="sy2">*</span> PI<span class="br0">)</span><span class="sy4">;</span> <span class="co1">// Euler's formula</span>
<a href="../io/fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"exp(I*PI) = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="complex/creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z3<span class="br0">)</span>, <a href="complex/cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z3<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
 
<span class="kw4">double</span> <a href="complex/complex.html"><span class="kw743">complex</span></a> z4 <span class="sy1">=</span> <span class="nu0">1</span><span class="sy2">+</span><span class="nu0">2</span><span class="sy2">*</span>I, z5 <span class="sy1">=</span> <span class="nu0">1</span><span class="sy2">-</span><span class="nu0">2</span><span class="sy2">*</span>I<span class="sy4">;</span> <span class="co1">// conjugates</span>
<a href="../io/fprintf.html"><span class="kw851">printf</span></a><span class="br0">(</span><span class="st0">"(1+2i)*(1-2i) = %.1f%+.1fi<span class="es1">\n</span>"</span>, <a href="complex/creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z4<span class="sy2">*</span>z5<span class="br0">)</span>, <a href="complex/cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z4<span class="sy2">*</span>z5<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span></pre></div></div>
<p>Output:
</p>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="text source-text"><pre class="de1">I * I = -1.0+0.0i
pow(I, 2) = -1.0+0.0i
exp(I*PI) = -1.0+0.0i
(1+2i)*(1-2i) = 5.0+0.0i</pre></div></div>
</div>
<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=c/numeric/complex&action=edit&section=3" title="Edit section: References">edit</a>]</span> <span class="mw-headline" id="References">References</span></h3>
<div class="t-ref-std-11">
<ul><li> C11 standard (ISO/IEC 9899:2011):
</li></ul>
<dl><dd><ul><li> 6.10.8.3/1/2 __STDC_NO_COMPLEX__ (p: 177)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 6.10.8.3/1/2 __STDC_IEC_559_COMPLEX__ (p: 177)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.3 Complex arithmetic <complex.h> (p: 188-199)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.3.1/2 __STDC_NO_COMPLEX__ (p: 188)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.25 Type-generic math <tgmath.h> (p: 373-375)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.31.1 Complex arithmetic <complex.h> (p: 455)
</li></ul>
</dd></dl>
<dl><dd><ul><li> B.2 Complex <complex.h> (p: 475-477)
</li></ul>
</dd></dl>
<dl><dd><ul><li> Annex G (normative) IEC 60559-compatible complex arithmetic (p: 532-545)
</li></ul>
</dd></dl>
<dl><dd><ul><li> G.1/1 __STDC_IEC_559_COMPLEX__ (p: 532)
</li></ul>
</dd></dl>
<div class="t-ref-std-c99">
<ul><li> C99 standard (ISO/IEC 9899:1999):
</li></ul>
<dl><dd><ul><li> 6.10.8/2 __STDC_IEC_559_COMPLEX__ (p: 161)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.3 Complex arithmetic <complex.h> (p: 170-180)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.22 Type-generic math <tgmath.h> (p: 335-337)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.26.1 Complex arithmetic <complex.h> (p: 401)
</li></ul>
</dd></dl>
<dl><dd><ul><li> B.2 Complex <complex.h> (p: 419-420)
</li></ul>
</dd></dl>
<dl><dd><ul><li> Annex G (informative) IEC 60559-compatible complex arithmetic (p: 467-480)
</li></ul>
</dd></dl>
<dl><dd><ul><li> G.1/1 __STDC_IEC_559_COMPLEX__ (p: 467)
</li></ul>
</dd></dl>
</div>
<h3><span class="editsection">[<a href="http://en.cppreference.com/mwiki/index.php?title=c/numeric/complex&action=edit&section=4" title="Edit section: See also">edit</a>]</span> <span class="mw-headline" id="See_also">See also</span></h3>
<table class="t-dsc-begin">
<tr class="t-dsc">
<td colspan="2"> <div class="t-dsc-see"><span><a href="../../cpp/numeric/complex.html" title="cpp/numeric/complex">C++ documentation</a></span> for <span class="t-dsc-see-tt"><span>Complex number arithmetic</span></span></div>
</td></tr>
</table></div>
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