Answer to Question #349055 in Complex Analysis for Mapula Advice

Question

If z=8(cos5π/3+isin5π/3), then z6 is equal to

Answer 1

$$z^6=8^6\big(\cos(6(\dfrac{5\pi}{3}))+i\sin(6(\dfrac{5\pi}{3}))\big)$$ $$=262144\big(\cos(10\pi)+i\sin(10\pi)\big)=262144$$