Answer
$ cos54^\circ+i\ sin54^\circ$, $ cos126^\circ+i\ sin126^\circ$, $ cos198^\circ+i\ sin198^\circ$, $ cos270^\circ+i\ sin270^\circ$, $ cos342^\circ+i\ sin342^\circ$.
Work Step by Step
Based on the given conditions, we have:
$-i=cos270^\circ+i\ sin270^\circ)$, $(i)^{1/5}=cos(\frac{360k+270}{5})^\circ+i\ sin(\frac{360k+270}{5})^\circ)$, $k=0, z_0= cos54^\circ+i\ sin54^\circ$, $k=1, z_1= cos126^\circ+i\ sin126^\circ$, $k=2, z_2= cos198^\circ+i\ sin198^\circ$, $k=3, z_3= cos270^\circ+i\ sin270^\circ$, $k=4, z_4= cos342^\circ+i\ sin342^\circ$.
