Answer
$w_0=2(cos~\frac{4\pi}{15}+i~sin~\frac{4\pi}{15})$
$w_1=2(cos~\frac{2\pi}{3}+i~sin~\frac{2\pi}{3})=-1+\sqrt 3i$
$w_2=2(cos~\frac{16\pi}{15}+i~sin~\frac{16\pi}{15})$
$w_3=2(cos~\frac{22\pi}{15}+i~sin~\frac{22\pi}{15})$
$w_4=2(cos~\frac{28\pi}{15}+i~sin~\frac{28\pi}{15})$
Work Step by Step
$r=|z|=\sqrt {a^2+b^2}=\sqrt {(-16)^2+(-16\sqrt 3)^2}=\sqrt {1024}=32$
$tan~θ=\frac{b}{a}=\frac{-16\sqrt 3}{-16}=\sqrt 3$
$θ=\frac{4\pi}{3}$
Polar form:
$z=32(cos~\frac{4\pi}{3}+i~sin~\frac{4\pi}{3})$
$w_k=\sqrt[5]{32}[cos(\frac{\frac{4\pi}{3}+2k\pi}{5})+i~sin(\frac{\frac{4\pi}{3}+2k\pi}{5})]$
$w_0=2(cos~\frac{4\pi}{15}+i~sin~\frac{4\pi}{15})$
$w_1=2(cos~\frac{2\pi}{3}+i~sin~\frac{2\pi}{3})=-1+\sqrt 3i$
$w_2=2(cos~\frac{16\pi}{15}+i~sin~\frac{16\pi}{15})$
$w_3=2(cos~\frac{22\pi}{15}+i~sin~\frac{22\pi}{15})$
$w_4=2(cos~\frac{28\pi}{15}+i~sin~\frac{28\pi}{15})$
