Suppose z^3=2+2 i, where i=\sqrt{-1}. The product of all possible values of the real part of z can be written in the form \frac{P}{q} where p and q are relatively prime positive integers. Find p+q.
Suppose z^3=2+2 i, where i=\sqrt{-1}. The product of all possible values of the real part of z can be written in the form \frac{P}{q} where p and q are relatively prime positive integers. Find p+q.