Answer
$ 2\sqrt[6] 2(cos75^\circ+i\ sin75^\circ)$, $ 2\sqrt[6] 2(cos195^\circ+i\ sin195^\circ)$, $ 2\sqrt[6] 2(cos315^\circ+i\ sin315^\circ)$.
Work Step by Step
Based on the given conditions, we have:
$-8-8i=8\sqrt 2(cos225^\circ+i\ sin225^\circ)$, $(-8-8i)^{1/3}=2\sqrt[6] 2(cos(\frac{360k+225}{3})^\circ+i\ sin(\frac{360k+225}{3})^\circ)$, $k=0, z_0=2\sqrt[6] 2(cos75^\circ+i\ sin75^\circ)$, $k=1, z_1=2\sqrt[6] 2(cos195^\circ+i\ sin195^\circ)$, $k=2, z_2=2\sqrt[6] 2(cos315^\circ+i\ sin315^\circ)$.
