Answer
$w_0=1$
$w_1=\frac{1}{2}+\frac{\sqrt 3}{2}i$
$w_2=-\frac{1}{2}+\frac{\sqrt 3}{2}i$
$w_3=-1$
$w_4=-\frac{1}{2}-\frac{\sqrt 3}{2}i$
$w_5=\frac{1}{2}-\frac{\sqrt 3}{2}i$
Work Step by Step
$r=|z|=1$
$θ=0~~$ (Posiative real axis)
Polar form:
$z=1=1(cos~0+i~sin~0)$
$w_k=\sqrt {1}[cos(\frac{0+2k\pi}{6})+i~sin(\frac{0+2k\pi}{6})]$
$w_0=1(cos~0+i~sin~0)=1$
$w_1=1(cos~\frac{\pi}{3}+i~sin~\frac{\pi}{3})=\frac{1}{2}+\frac{\sqrt 3}{2}i$
$w_2=1(cos~\frac{2\pi}{3}+i~sin~\frac{2\pi}{3})=-\frac{1}{2}+\frac{\sqrt 3}{2}i$
$w_3=1(cos~\pi+i~sin~\pi)=-1$
$w_4=1(cos~\frac{4\pi}{3}+i~sin~\frac{4\pi}{3})=-\frac{1}{2}-\frac{\sqrt 3}{2}i$
$w_5=1(cos~\frac{5\pi}{3}+i~sin~\frac{5\pi}{3})=\frac{1}{2}-\frac{\sqrt 3}{2}i$
