Answer
(a) $ 16(cos50^\circ+i\ sin50^\circ)$
(b) $ 2\sqrt 3+2i$
(c) $ 4\sqrt 3+4i$
Work Step by Step
Given $w=8(cos40^\circ+i\ sin40^\circ)$ and $z=2(cos10^\circ+i\ sin10^\circ)$, we have:
(a) $wz=(8)(2)(cos(40+10)^\circ+i\ sin(40+10)^\circ)=16(cos50^\circ+i\ sin50^\circ)$
(b) $\frac{w}{z}=\frac{8}{2}(cos(40-10)^\circ+i\ sin(40-10)^\circ)=4(cos30^\circ+i\ sin30^\circ)=4(\frac{\sqrt 3}{2}+i\ \frac{1}{2})=2\sqrt 3+2i$
(c) $z^3=2^3(cos(3\times10)^\circ+i\ sin(3\times10)^\circ)=8(cos30^\circ+i\ sin30^\circ)=8(\frac{\sqrt 3}{2}+i\ \frac{1}{2})=4\sqrt 3+4i$
