This equation is a quadratic in z3...
(z3 - 4)(z3 + 2)
Use De Moivre's theorem to express the roots in polar form...although you really don't need De Moivre's theorem since the cube roots are simply obtained using the 3 cube roots of 1.
Yes...you need to use De Moivre's Theorem on each factor.
However, a short cut is that the 3 solutions of z3=R are R1/3 times 1, times ω, and times ω2.
.....ω and ω2 are the 2 complex roots of 1.