Originally Posted by

**romsek** $\Large x + \imath y = \rho e^{\imath \theta}$

where

$\large \rho = \sqrt{x^2 + y^2}$

$\large \theta = \arg(x,y) = \arctan(y,x)$ where $\arctan(y,x)=\arctan\left(\frac y x\right)$ with the result adjusted for the correct quadrant.

Then $\Large \left(\rho e^{\imath \theta}\right)^k = \rho^k e^{\imath k \theta}$

Also if you have two complex numbers in polar form their product is given by

$\Large \left(\rho_1 e^{\imath \theta_1}\right)\left(\rho_2 e^{\imath \theta_2}\right)=\rho_1 \rho_2 e^{\imath(\theta_1+\theta_2)}$

that should be all you need to do your calculation