Answer
$w_0=cos~\frac{\pi}{10}+i~sin~\frac{\pi}{10}$
$w_1=i$
$w_2=cos~\frac{9\pi}{10}+i~sin~\frac{9\pi}{10}$
$w_3=cos~\frac{13\pi}{10}+i~sin~\frac{13\pi}{10}$
$w_4=cos~\frac{17\pi}{10}+i~sin~\frac{17\pi}{10}$
Work Step by Step
$r=|z|=1$
$θ=\frac{\pi}{2}~~$ (Positive imaginary axis)
Polar form:
$z=1(cos~\frac{\pi}{2}+i~sin~\frac{\pi}{2})$
$w_k=\sqrt[5] 1[cos(\frac{\frac{\pi}{2}+2k\pi}{5})+i~sin(\frac{\frac{\pi}{2}+2k\pi}{5})]$
$w_0=1(cos~\frac{\pi}{10}+i~sin~\frac{\pi}{10})$
$w_1=1(cos~\frac{\pi}{2}+i~sin~\frac{\pi}{2})=i$
$w_2=1(cos~\frac{9\pi}{10}+i~sin~\frac{9\pi}{10})$
$w_3=1(cos~\frac{13\pi}{10}+i~sin~\frac{13\pi}{10})$
$w_4=1(cos~\frac{17\pi}{10}+i~sin~\frac{17\pi}{10})$
