Answer
$[{cis 180^{\circ},cis 300^{\circ},cis 420^{\circ}}]$
Work Step by Step
Given: $x^{3}+1=0$
or $x^{3}=-1$
$-1$ can be written in trigonometric form as:
$-1=-1+0.i=1(\cos 180^{\circ}+\sin 180^{\circ})$
Absolute value of third root is given as $\sqrt[3] 1=1$
Now, the arguments can be given as:
$k=0,1,2$
Roots: $1(\cos 180^{\circ}+\sin 180^{\circ})$,$1(\cos 300^{\circ}+\sin 300^{\circ})$,$1(\cos 420^{\circ}+\sin 420^{\circ})$,
Solution set of the equation can be written as:
$[{cis 180^{\circ},cis 300^{\circ},cis 420^{\circ}}]$
