Answer
$zw=8(cos\frac{15\pi}{16}+i\ sin\frac{15\pi}{16}), \frac{z}{w}= 2(cos\frac{29\pi}{16}+i\ sin\frac{29\pi}{16})$
Work Step by Step
Given $z=4(cos\frac{3\pi}{8}+i\ sin\frac{3\pi}{8})$ and $w=2(cos\frac{9\pi}{16}+i\ sin\frac{9\pi}{16})$, we have:
1. $zw=8(cos(\frac{3\pi}{8}+\frac{9\pi}{16})+i\ sin(\frac{3\pi}{8}+\frac{9\pi}{16}))=8(cos\frac{15\pi}{16}+i\ sin\frac{15\pi}{16})$
2. $\frac{z}{w}=2(cos(\frac{3\pi}{8}-\frac{9\pi}{16})+i\ sin(\frac{3\pi}{8}-\frac{9\pi}{16}))=2(cos\frac{-3\pi}{16}+i\ sin\frac{-3\pi}{16})=2(cos\frac{29\pi}{16}+i\ sin\frac{29\pi}{16})$
