Answer
$zw=4(\cos({\frac{9\pi}{40})}+i\sin{(\frac{9\pi}{40}})$
and
$\frac{z}{w}=(\cos({\frac{\pi}{40})}+i\sin{\frac{\pi}{40}})$.
Work Step by Step
We know that if $z=a(\cos{\alpha}+i\sin{\alpha})$ and $w=b(\cos{\beta}+i\sin{\beta})$, then
$zw=ab(\cos({\alpha+\beta)}+i\sin{(\alpha+\beta})$ and
$\frac{z}{w}=\frac{a}{b}(\cos({\alpha-\beta)}+i\sin{(\alpha-\beta})$.
Hence here:
$zw=(2)(12(\cos({\frac{\pi}{8}+\frac{\pi}{10})}+i\sin{(\frac{\pi}{8}+\frac{\pi}{10}})\\zw=4(\cos({\frac{9\pi}{40})}+i\sin{(\frac{9\pi}{40}})$
and
$\frac{z}{w}=\frac{2}{2}(\cos({\frac{\pi}{8}-\frac{\pi}{10})}+i\sin{\frac{\pi}{8}-\frac{\pi}{10}})\\\frac{z}{w}=(\cos({\frac{\pi}{40})}+i\sin{\frac{\pi}{40}})$.
