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### 5.4 Elementary Complex Functions

Function: gsl_complex gsl_complex_sqrt (gsl_complex z)

This function returns the square root of the complex number z, \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, z^a. This is computed as \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, z^x.

Function: gsl_complex gsl_complex_exp (gsl_complex z)

This function returns the complex exponential of the complex number z, \exp(z).

Function: gsl_complex gsl_complex_log (gsl_complex z)

This function returns the complex natural logarithm (base e) of the complex number z, \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, \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, \log_b(z). This quantity is computed as the ratio \log(z)/\log(b).