GNU Scientific Library – Reference Manual: Properties of complex numbers

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### 5.2 Properties of complex numbers

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.