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

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<a name="Elementary-Complex-Functions"></a>
<div class="header">
<p>
Next: <a href="Complex-Trigonometric-Functions.html#Complex-Trigonometric-Functions" accesskey="n" rel="next">Complex Trigonometric Functions</a>, Previous: <a href="Complex-arithmetic-operators.html#Complex-arithmetic-operators" accesskey="p" rel="previous">Complex arithmetic operators</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Elementary-Complex-Functions-1"></a>
<h3 class="section">5.4 Elementary Complex Functions</h3>

<dl>
<dt><a name="index-gsl_005fcomplex_005fsqrt"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_sqrt</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><a name="index-square-root-of-complex-number"></a>
<p>This function returns the square root of the complex number <var>z</var>,
<em>\sqrt z</em>. The branch cut is the negative real axis. The result
always lies in the right half of the complex plane.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005fsqrt_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_sqrt_real</strong> <em>(double <var>x</var>)</em></dt>
<dd><p>This function returns the complex square root of the real number
<var>x</var>, where <var>x</var> may be negative.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fcomplex_005fpow"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_pow</strong> <em>(gsl_complex <var>z</var>, gsl_complex <var>a</var>)</em></dt>
<dd><a name="index-power-of-complex-number"></a>
<a name="index-exponentiation-of-complex-number"></a>
<p>The function returns the complex number <var>z</var> raised to the complex
power <var>a</var>, <em>z^a</em>. This is computed as <em>\exp(\log(z)*a)</em>
using complex logarithms and complex exponentials.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005fpow_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_pow_real</strong> <em>(gsl_complex <var>z</var>, double <var>x</var>)</em></dt>
<dd><p>This function returns the complex number <var>z</var> raised to the real
power <var>x</var>, <em>z^x</em>.
</p></dd></dl>


<dl>
<dt><a name="index-gsl_005fcomplex_005fexp"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_exp</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex exponential of the complex number
<var>z</var>, <em>\exp(z)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005flog"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_log</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><a name="index-logarithm-of-complex-number"></a>
<p>This function returns the complex natural logarithm (base <em>e</em>) of
the complex number <var>z</var>, <em>\log(z)</em>.  The branch cut is the
negative real axis. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005flog10"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_log10</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex base-10 logarithm of
the complex number <var>z</var>, <em>\log_10 (z)</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005flog_005fb"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_log_b</strong> <em>(gsl_complex <var>z</var>, gsl_complex <var>b</var>)</em></dt>
<dd><p>This function returns the complex base-<var>b</var> logarithm of the complex
number <var>z</var>, <em>\log_b(z)</em>. This quantity is computed as the ratio
<em>\log(z)/\log(b)</em>.
</p></dd></dl>





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