## Elementary Complex Functions

Function: gsl_complex gsl_complex_sqrt (gsl_complex z)
This function returns the square root of the complex number z, @math{\sqrt z}. The branch cut is the negative real axis. The result always lies in the right half of the complex plane.

Function: gsl_complex gsl_complex_sqrt_real (double x)
This function returns the complex square root of the real number x, where x may be negative.

Function: gsl_complex gsl_complex_pow (gsl_complex z, gsl_complex a)
The function returns the complex number z raised to the complex power a, @math{z^a}. This is computed as @math{\exp(\log(z)*a)} using complex logarithms and complex exponentials.

Function: gsl_complex gsl_complex_pow_real (gsl_complex z, double x)
This function returns the complex number z raised to the real power x, @math{z^x}.

Function: gsl_complex gsl_complex_exp (gsl_complex z)
This function returns the complex exponential of the complex number z, @math{\exp(z)}.

Function: gsl_complex gsl_complex_log (gsl_complex z)
This function returns the complex natural logarithm (base @math{e}) of the complex number z, @math{\log(z)}. The branch cut is the negative real axis.

Function: gsl_complex gsl_complex_log10 (gsl_complex z)
This function returns the complex base-10 logarithm of the complex number z, @c{$\log_{10}(z)$} @math{\log_10 (z)}.

Function: gsl_complex gsl_complex_log_b (gsl_complex z, gsl_complex b)
This function returns the complex base-b logarithm of the complex number z, @math{\log_b(z)}. This quantity is computed as the ratio @math{\log(z)/\log(b)}.