Answer
$w_0=2\sqrt 2[cos(\frac{\pi}{12})+i~sin(\frac{\pi}{12})]$
$w_1=2\sqrt 2[cos(\frac{13\pi}{12})+i~sin(\frac{13\pi}{12})]$
Work Step by Step
$r=|z|=\sqrt {a^2+b^2}=\sqrt {(4\sqrt 3)^2+4^2}=\sqrt {64}=8$
$tan~θ=\frac{b}{a}=\frac{\sqrt 3}{3}$
$θ=\frac{\pi}{6}$
Polar form:
$z=8(cos\frac{\pi}{6}~+i~sin\frac{\pi}{6})$
$w_k=\sqrt 8[cos(\frac{\frac{\pi}{6}+2k\pi}{2})+i~sin(\frac{\frac{\pi}{6}+2k\pi}{2})]$
$w_0=2\sqrt 2[cos(\frac{\pi}{12})+i~sin(\frac{\pi}{12})]$
$w_1=2\sqrt 2[cos(\frac{13\pi}{12})+i~sin(\frac{13\pi}{12})]$
