For 1/5^(1/2+12*I) and the above commands one gets -12*ln(5)+6*Pi as argument. Essentially I agree. But you add 2 vectors in the plane (in polar coordinates), which can be "done" by ruler and pencile. And you ask for the angle (Maple ...) r*exp(I*phi) + s*exp(I*psi); eval(%, s=1); # some scaling to unit circle: assume s=1 argument(%); convert(%, arctan); evalc(%); arctan(r*sin(phi)+sin(psi),r*cos(phi)+cos(psi)); This is arctan with certain "sign rule" Without further assumptions I would not expect more "structure" in a result: One adds 2 vectors, their resulting angle is expressed in terms of trigonometrics.