Answer
$[5(cos~20°+i~sin~20°)]^3=\frac{125}{2}+\frac{125\sqrt 3}{2}i$
Work Step by Step
DeMoivre's Theorem:
If $z=r(cos θ+i~sin θ)$, then
$z^n=r^n(cos~nθ+i~sin~nθ)$
$z=5(cos~20°+i~sin~20°)$
$z^3=5^3[cos~(3 ·20°)+i~sin~(3 ·20°)]$
$z^3=125(cos~60°+i~sin~60°)$
$z^3=125(\frac{1}{2}+i\frac{\sqrt 3}{2})$
$z^3=\frac{125}{2}+\frac{125\sqrt 3}{2}i$
