Answer
$z_0=\frac{\sqrt 3}{2}+\frac{1}{2}i$
$z_1=-\frac{\sqrt 3}{2}+\frac{1}{2}i$
$z_2=-i$
Work Step by Step
$z^3-i=0$
$z^3=i$
$r=|i|=1$. Also $i$ lies in the positive imaginary axis.
Polar form of $i$:
$1(cos~\frac{\pi}{2}+i~sin~\frac{\pi}{2})$
$z_k=\sqrt[3]{1}[cos(\frac{\frac{\pi}{2}+2k\pi}{3})+i~sin(\frac{\frac{\pi}{2}+2k\pi}{3})]$
$z_0=1(cos~\frac{\pi}{6}+i~sin~\frac{\pi}{6})=\frac{\sqrt 3}{2}+\frac{1}{2}i$
$z_1=1(cos~\frac{5\pi}{6}+i~sin~\frac{5\pi}{6})=-\frac{\sqrt 3}{2}+\frac{1}{2}i$
$z_2=1(cos~\frac{3\pi}{2}+i~sin~\frac{3\pi}{2})=-i$
