a) Express -4√3 - 4i in exact polar form.
b) Find the cube roots of -4√3 - 4i.
c) Show that the cubic equation z3 - 3√3iz2 - 9z + 3√3i = -4√3 - 4i can be written in the form (z - w)3 = -4√3 - 4i where w is a complex number.
With part c, I know I have to somehow use my answer(s) from part b in order to solve for w, but I'm not sure exactly how. I was thinking along the lines of:
(z - w)3 = -4√3 - 4i
w = z - 3√(-4√3 - 4i)
Do I have to express the cube roots of -4√3 - 4i from part b in cartesian form? If so, how do I go about it (considering there are 3 solutions)?