Answer
$w_0=\frac{\sqrt 3}{2}+\frac{1}{2}i$
$w_1=-\frac{\sqrt 3}{2}+\frac{1}{2}i$
$w_2=-i$
Work Step by Step
$r=|z|=1$
$θ=\frac{\pi}{2}~~$ (Positive imaginary axis)
Polar form:
$z=1(cos~\frac{\pi}{2}+i~sin~\frac{\pi}{2})$
$w_k=\sqrt[3] 1[cos(\frac{\frac{\pi}{2}+2k\pi}{3})+i~sin(\frac{\frac{\pi}{2}+2k\pi}{3})]$
$w_0=1(cos~\frac{\pi}{6}+i~sin~\frac{\pi}{6})=\frac{\sqrt 3}{2}+\frac{1}{2}i$
$w_1=1(cos~\frac{5\pi}{6}+i~sin~\frac{5\pi}{6})=-\frac{\sqrt 3}{2}+\frac{1}{2}i$
$w_2=1(cos~\frac{3\pi}{2}+i~sin~\frac{3\pi}{2})=-i$
