Answer
$w_0=cos~\frac{\pi}{16}+i~sin~\frac{\pi}{16}$
$w_1=cos~\frac{5\pi}{16}+i~sin~\frac{5\pi}{16}$
$w_2=cos~\frac{9\pi}{16}+i~sin~\frac{9\pi}{16}$
$w_3=cos~\frac{13\pi}{16}+i~sin~\frac{13\pi}{16}$
$w_4=cos~\frac{17\pi}{16}+i~sin~\frac{17\pi}{16}$
$w_5=cos~\frac{21\pi}{16}+i~sin~\frac{21\pi}{16}$
$w_6=cos~\frac{25\pi}{16}+i~sin~\frac{25\pi}{16}$
$w_7=cos~\frac{29\pi}{16}+i~sin~\frac{29\pi}{16}$
Work Step by Step
$r=|z|=1$
$θ=\frac{\pi}{2}~~$ (Positive imaginary axis)
Polar form:
$z=1=1(cos~\frac{\pi}{2}+i~sin~\frac{\pi}{2})$
$w_k=\sqrt[8] {1}[cos(\frac{\frac{\pi}{2}+2k\pi}{8})+i~sin(\frac{\frac{\pi}{2}+2k\pi}{8})]$
$w_0=1(cos~\frac{\pi}{16}+i~sin~\frac{\pi}{16})$
$w_1=1(cos~\frac{5\pi}{16}+i~sin~\frac{5\pi}{16})$
$w_2=1(cos~\frac{9\pi}{16}+i~sin~\frac{9\pi}{16})$
$w_3=1(cos~\frac{13\pi}{16}+i~sin~\frac{13\pi}{16})$
$w_4=1(cos~\frac{17\pi}{16}+i~sin~\frac{17\pi}{16})$
$w_5=1(cos~\frac{21\pi}{16}+i~sin~\frac{21\pi}{16})$
$w_6=1(cos~\frac{25\pi}{16}+i~sin~\frac{25\pi}{16})$
$w_7=1(cos~\frac{29\pi}{16}+i~sin~\frac{29\pi}{16})$
