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<title>Elementary Complex Functions - GNU Scientific Library -- Reference Manual</title>
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<a name="Elementary-Complex-Functions"></a>
Next: <a rel="next" accesskey="n" href="Complex-Trigonometric-Functions.html">Complex Trigonometric Functions</a>,
Previous: <a rel="previous" accesskey="p" href="Complex-arithmetic-operators.html">Complex arithmetic operators</a>,
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<h3 class="section">5.4 Elementary Complex Functions</h3>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_sqrt</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fsqrt-170"></a></var><br>
<blockquote><p><a name="index-square-root-of-complex-number-171"></a>This function returns the square root of the complex number <var>z</var>,
\sqrt z. The branch cut is the negative real axis. The result
always lies in the right half of the complex plane.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_sqrt_real</b> (<var>double x</var>)<var><a name="index-gsl_005fcomplex_005fsqrt_005freal-172"></a></var><br>
<blockquote><p>This function returns the complex square root of the real number
<var>x</var>, where <var>x</var> may be negative.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_pow</b> (<var>gsl_complex z, gsl_complex a</var>)<var><a name="index-gsl_005fcomplex_005fpow-173"></a></var><br>
<blockquote><p><a name="index-power-of-complex-number-174"></a><a name="index-exponentiation-of-complex-number-175"></a>The function returns the complex number <var>z</var> raised to the complex
power <var>a</var>, z^a. This is computed as \exp(\log(z)*a)
using complex logarithms and complex exponentials.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_pow_real</b> (<var>gsl_complex z, double x</var>)<var><a name="index-gsl_005fcomplex_005fpow_005freal-176"></a></var><br>
<blockquote><p>This function returns the complex number <var>z</var> raised to the real
power <var>x</var>, z^x.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_exp</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fexp-177"></a></var><br>
<blockquote><p>This function returns the complex exponential of the complex number
<var>z</var>, \exp(z).
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_log</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005flog-178"></a></var><br>
<blockquote><p><a name="index-logarithm-of-complex-number-179"></a>This function returns the complex natural logarithm (base e) of
the complex number <var>z</var>, \log(z). The branch cut is the
negative real axis.
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_log10</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005flog10-180"></a></var><br>
<blockquote><p>This function returns the complex base-10 logarithm of
the complex number <var>z</var>, <!-- {$\log_{10}(z)$} -->
\log_10 (z).
</p></blockquote></div>
<div class="defun">
— Function: gsl_complex <b>gsl_complex_log_b</b> (<var>gsl_complex z, gsl_complex b</var>)<var><a name="index-gsl_005fcomplex_005flog_005fb-181"></a></var><br>
<blockquote><p>This function returns the complex base-<var>b</var> logarithm of the complex
number <var>z</var>, \log_b(z). This quantity is computed as the ratio
\log(z)/\log(b).
</p></blockquote></div>
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