Answer
$w^3$
= $- 864 - 864\sqrt{3}i$
Work Step by Step
$w = 12(cos80^\circ + isin80^\circ) = 12cis80^\circ$
Now, $w^3$
= $(12cis80^\circ)^3$
= $12^3 cis 3\cdot 80^\circ$ (De Moivre’s Theorem)
= $1728cis240^\circ$
= $1728(cos240^\circ + isin240^\circ)$
= $1728(-\frac{1}{2} - \frac{\sqrt{3}}{2} i)$
= $- 864 - 864\sqrt{3}i$
