CPM Homework Help : PC3 Problem 12-70

Use De Moivre’s Theorem to evaluate $z^{6}$ for $z=2\left(\cos\left(\frac{\pi}{6}\right)+i\sin\left(\frac{\pi}{6}\right)\right)$ .

Hint:

$z^{6} = 6 \cdot 2 \Big(\cos(6 \cdot \frac{\pi}{6}) + i \sin (6 \cdot \frac{\pi}{6})\Big)$