Answer
$zw= 4\sqrt 2(cos15^\circ+i\ sin15^\circ), \frac{z}{w}= \sqrt 2(cos75^\circ+i\ sin75^\circ)$
Work Step by Step
Given $z=2+2i=2\sqrt 2(cos45^\circ+i\ sin45^\circ)$ and $w=\sqrt 3-i=2(cos330^\circ+i\ sin330^\circ)$, we have:
1. $zw=4\sqrt 2(cos(45^\circ+330^\circ)+i\ sin(45^\circ+330^\circ))=4\sqrt 2(cos15^\circ+i\ sin15^\circ)$
2. $\frac{z}{w}=\sqrt 2(cos(45^\circ-330^\circ)+i\ sin(45^\circ-330^\circ))=\sqrt 2(cos(45^\circ+360^\circ-330^\circ)+i\ sin(45^\circ+360^\circ-330^\circ))=\sqrt 2(cos75^\circ+i\ sin75^\circ)$
