## Algebra and Trigonometry 10th Edition

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