Answer
$w_0=\sqrt[6] 2(cos~\frac{\pi}{12}+i~sin~\frac{\pi}{12})$
$w_1=\sqrt[6] 2(cos~\frac{3\pi}{4}+i~sin~\frac{3\pi}{4})$
$w_2=\sqrt[6] 2(cos~\frac{17\pi}{12}+i~sin~\frac{17\pi}{12})$
Work Step by Step
$r=|z|=\sqrt {a^2+b^2}=\sqrt {1^2+1^2}=\sqrt 2$
$tan~θ=\frac{b}{a}=1$
$θ=\frac{\pi}{4}$
Polar form:
$z=\sqrt 2(cos~\frac{\pi}{4}+i~sin~\frac{\pi}{4})$
$w_k=\sqrt[3] {\sqrt 2}[cos(\frac{\frac{\pi}{4}+2k\pi}{3})+i~sin(\frac{\frac{\pi}{4}+2k\pi}{3})]$
$w_0=\sqrt[6] 2(cos~\frac{\pi}{12}+i~sin~\frac{\pi}{12})$
$w_1=\sqrt[6] 2(cos~\frac{3\pi}{4}+i~sin~\frac{3\pi}{4})$
$w_2=\sqrt[6] 2(cos~\frac{17\pi}{12}+i~sin~\frac{17\pi}{12})$
