How do I reduce (2i+2)/(1-i) with step-by-step please? I need a step by step answer on how to do this. What I've been doing is converting the top to $2e^{i(\pi/4)}$ and the bottom to $\sqrt2e^{i(-\pi/4)}$. I know the answer is $2e^{i(\pi/2)}$ and the angle makes sense but obviously I'm doing something wrong with the coefficients. I suspect maybe only the real part goes into calculating the amplitude but I can't be sure.

Try multiplying the numerator and denominator by $1+i$. This will give you $\frac{(2i+2)(1+i)}{1^2+1^2}$. Then, FOIL the numerator and note $i^2=-1$. 
