Answer
$w_0=2(cos~\frac{\pi}{9}+i~sin~\frac{\pi}{9})$
$w_1=2(cos~\frac{7\pi}{9}+i~sin~\frac{7\pi}{9})$
$w_2=2(cos~\frac{13\pi}{9}+i~sin~\frac{13\pi}{9})$
Work Step by Step
$r=|z|=\sqrt {a^2+b^2}=\sqrt {4^2+(4\sqrt 3)^2}=\sqrt {64}=8$
$tan~θ=\frac{b}{a}=\frac{4\sqrt 3}{4}=\sqrt 3$
$θ=\frac{\pi}{3}$
Polar form:
$z=8(cos~\frac{\pi}{3}+i~sin~\frac{\pi}{3})$
$w_k=\sqrt[3] {8}[cos(\frac{\frac{\pi}{3}+2k\pi}{3})+i~sin(\frac{\frac{\pi}{3}+2k\pi}{3})]$
$w_0=2(cos~\frac{\pi}{9}+i~sin~\frac{\pi}{9})$
$w_1=2(cos~\frac{7\pi}{9}+i~sin~\frac{7\pi}{9})$
$w_2=2(cos~\frac{13\pi}{9}+i~sin~\frac{13\pi}{9})$
