— Function: double gsl_complex_arg (gsl_complex z)

This function returns the argument of the complex number z, \arg(z), where -\pi < \arg(z) <= \pi.

— Function: double gsl_complex_abs (gsl_complex z)

This function returns the magnitude of the complex number z, |z|.

— Function: double gsl_complex_abs2 (gsl_complex z)

This function returns the squared magnitude of the complex number z, |z|^2.

— Function: double gsl_complex_logabs (gsl_complex z)

This function returns the natural logarithm of the magnitude of the complex number z, \log|z|. It allows an accurate evaluation of \log|z| when |z| is close to one. The direct evaluation of log(gsl_complex_abs(z)) would lead to a loss of precision in this case.