Answer
$w_0=3[cos(\frac{3\pi}{8})+i~sin(\frac{3\pi}{8})]$
$w_1=3[cos(\frac{7\pi}{8})+i~sin(\frac{7\pi}{8})]$
$w_2=3[cos(\frac{11\pi}{8})+i~sin(\frac{11\pi}{8})]$
$w_3=3[cos(\frac{15\pi}{8})+i~sin(\frac{15\pi}{8})]$
Work Step by Step
$r=|z|=81$
$θ=\frac{3\pi}{2}~~$ (Negative imaginary axis)
Polar form:
$z=81(cos\frac{3\pi}{2}+i~sin\frac{3\pi}{2})$
$w_k=\sqrt[4] {81}[cos(\frac{\frac{3\pi}{2}+2k\pi}{4})+i~sin(\frac{\frac{3\pi}{2}+2k\pi}{4})]$
$w_0=3[cos(\frac{3\pi}{8})+i~sin(\frac{3\pi}{8})]$
$w_1=3[cos(\frac{7\pi}{8})+i~sin(\frac{7\pi}{8})]$
$w_2=3[cos(\frac{11\pi}{8})+i~sin(\frac{11\pi}{8})]$
$w_3=3[cos(\frac{15\pi}{8})+i~sin(\frac{15\pi}{8})]$
