A complex number can be described by two real coordinates. One may use rectangular coordinates and gets z = x+I*y, where x = creal(z) and y = cimag(z).
Or one may use polar coordinates and gets z = r*cexp(I*a) where r = cabs(z) is the "radius", the "modulus", the absolute value of z, and a = carg(z) is the "phase angle", the argument of z.
One has carg(z) = atan(creal(z) / cimag(z)).
The return value is the range of [-pi,pi].