Answer
$zw=4(cos\frac{9\pi}{40}+i\ sin\frac{9\pi}{40}), \frac{z}{w}=cos\frac{\pi}{40}+i\ sin\frac{\pi}{40}$
Work Step by Step
Given $z=2(cos\frac{\pi}{8}+i\ sin\frac{\pi}{8})$ and $w=2(cos\frac{\pi}{10}+i\ sin\frac{\pi}{10})$, we have:
1. $zw=4(cos(\frac{\pi}{8}+\frac{\pi}{10})+i\ sin(\frac{\pi}{8}+\frac{\pi}{10}))=4(cos\frac{9\pi}{40}+i\ sin\frac{9\pi}{40})$
2. $\frac{z}{w}=cos(\frac{\pi}{8}-\frac{\pi}{10})+i\ sin(\frac{\pi}{8}-\frac{\pi}{10})=cos\frac{\pi}{40}+i\ sin\frac{\pi}{40}$
