If you do z abi and w c di and then find the modulus of both sides you will be left with ac bd . Hopefully you know this if not I can show you . Then I knew that argzargw argzw . I then proceeded to find out what abicdi was . If I multiply top and bottom with the complex conjugate cdi I will getacbciadibdc 2 d 2 Now using the fact that ac bd the real parts of the real parts of the numerator will disappear . Therefore I have ibcadc 2 d 2 SInce this is just a imaginary number that does not have a real part its argument has to be plus or minus pi 2 by definition . Hope this helped . Been a while since I last did complex numbers so I might have made some small errors , but I think the overall argument is correct at least .