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<title>GNU Scientific Library &ndash; Reference Manual: Complex Numbers</title>

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<a name="Complex-Numbers"></a>
<div class="header">
<p>
Next: <a href="Polynomials.html#Polynomials" accesskey="n" rel="next">Polynomials</a>, Previous: <a href="Mathematical-Functions.html#Mathematical-Functions" accesskey="p" rel="previous">Mathematical Functions</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Complex-Numbers-1"></a>
<h2 class="chapter">5 Complex Numbers</h2>
<a name="index-complex-numbers"></a>

<p>The functions described in this chapter provide support for complex
numbers.  The algorithms take care to avoid unnecessary intermediate
underflows and overflows, allowing the functions to be evaluated over 
as much of the complex plane as possible. 
</p>

<p>For multiple-valued functions the branch cuts have been chosen to follow
the conventions of Abramowitz and Stegun in the <cite>Handbook of
Mathematical Functions</cite>. The functions return principal values which are
the same as those in GNU Calc, which in turn are the same as those in
<cite>Common Lisp, The Language (Second Edition)</cite><a name="DOCF7" href="#FOOT7"><sup>7</sup></a> and the HP-28/48 series of
calculators.
</p>
<p>The complex types are defined in the header file <samp>gsl_complex.h</samp>,
while the corresponding complex functions and arithmetic operations are
defined in <samp>gsl_complex_math.h</samp>.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Representation-of-complex-numbers.html#Representation-of-complex-numbers" accesskey="1">Representation of complex numbers</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Properties-of-complex-numbers.html#Properties-of-complex-numbers" accesskey="2">Properties of complex numbers</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complex-arithmetic-operators.html#Complex-arithmetic-operators" accesskey="3">Complex arithmetic operators</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Elementary-Complex-Functions.html#Elementary-Complex-Functions" accesskey="4">Elementary Complex Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complex-Trigonometric-Functions.html#Complex-Trigonometric-Functions" accesskey="5">Complex Trigonometric Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Inverse-Complex-Trigonometric-Functions.html#Inverse-Complex-Trigonometric-Functions" accesskey="6">Inverse Complex Trigonometric Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complex-Hyperbolic-Functions.html#Complex-Hyperbolic-Functions" accesskey="7">Complex Hyperbolic Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Inverse-Complex-Hyperbolic-Functions.html#Inverse-Complex-Hyperbolic-Functions" accesskey="8">Inverse Complex Hyperbolic Functions</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Complex-Number-References-and-Further-Reading.html#Complex-Number-References-and-Further-Reading" accesskey="9">Complex Number References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
</table>

<div class="footnote">
<hr>
<h4 class="footnotes-heading">Footnotes</h4>

<h3><a name="FOOT7" href="#DOCF7">(7)</a></h3>
<p>Note that the
first edition uses different definitions.</p>
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