Answer
$w_0=-2\sqrt 2+2\sqrt 2i$
$w_1=2\sqrt 2-2\sqrt 2i$
Work Step by Step
$r=|z|=16$
$θ=\frac{3\pi}{2}~~$ (Negative imaginary axis)
Polar form:
$z=-16i=16(cos~\frac{3\pi}{2}+i~sin~\frac{3\pi}{2})$
$w_k=\sqrt {16}[cos(\frac{\frac{3\pi}{2}+2k\pi}{2})+i~sin(\frac{\frac{3\pi}{2}+2k\pi}{2})]$
$w_0=4(cos~\frac{3\pi}{4}+i~sin~\frac{3\pi}{4})=-2\sqrt 2+2\sqrt 2i$
$w_1=4(cos~\frac{7\pi}{4}+i~sin~\frac{7\pi}{4})=2\sqrt 2-2\sqrt 2i$
