Answer to Question #347965 in Complex Analysis for Busi

Question

If z=$8(\cos \frac{5\pi}{3}+i\sin \frac{5\pi}{3})$, then z⁶ is equal to

Answer 1

$$z^6=8^6\big(\cos(6(\dfrac{5\pi}{3}))+i\sin(6(\dfrac{5\pi}{3}))\big)$$

$$=262144\big(\cos(10\pi)+i\sin(10\pi)\big)=262144$$