I need help on this one.
Calculate (-2sqrt2i)^(2/3)
Note that this is the same as $\displaystyle \left[\left(-2\sqrt{2}i\right)^2\right]^{\frac{1}{3}}=\left(-8\right)^{\frac{1}{3}}$
Now can you find the three roots of unity? First convert this to exponential form and see if you can take it from there. If you still have issues, post back