Answer
$ cos18^\circ+i\ sin18^\circ$, $ cos90^\circ+i\ sin90^\circ$, $ cos162^\circ+i\ sin162^\circ$, $ cos234^\circ+i\ sin234^\circ$, $ cos306^\circ+i\ sin306^\circ$.
Work Step by Step
Based on the given conditions, we have:
$i=cos90^\circ+i\ sin90^\circ)$, $(i)^{1/5}=cos(\frac{360k+90}{5})^\circ+i\ sin(\frac{360k+90}{5})^\circ)$, $k=0, z_0= cos18^\circ+i\ sin18^\circ$, $k=1, z_1= cos90^\circ+i\ sin90^\circ$, $k=2, z_2= cos162^\circ+i\ sin162^\circ$, $k=3, z_3= cos234^\circ+i\ sin234^\circ$, $k=4, z_4= cos306^\circ+i\ sin306^\circ$.
