Answer
$ 2(cos67.5^\circ+i\ sin67.5^\circ)$, $ 2(cos157.5^\circ+i\ sin157.5^\circ)$, $ 2(cos247.5^\circ+i\ sin247.5^\circ)$, $ 2(cos337.5^\circ+i\ sin337.5^\circ)$.
Work Step by Step
Based on the given conditions, we have:
$-16i=16(cos270^\circ+i\ sin270^\circ)$, $(-16i)^{1/4}=2(cos(\frac{360k+270}{4})^\circ+i\ sin(\frac{360k+270}{4})^\circ)$, $k=0, z_0= 2(cos67.5^\circ+i\ sin67.5^\circ)$, $k=1, z_1= 2(cos157.5^\circ+i\ sin157.5^\circ)$, $k=2, z_2= 2(cos247.5^\circ+i\ sin247.5^\circ)$, $k=3, z_3= 2(cos337.5^\circ+i\ sin337.5^\circ)$.
