Answer
$zw=4[cos(\frac{\pi}{2})+isin(\frac{\pi}{2})]$,
$\frac{z}{w}=cos(-\pi/6)+isin(-\pi/6)]$,
$\frac{1}{z}=\frac{1}{2}[cos(-\frac{\pi}{6})+isin(-\frac{\pi}{6})]$
Work Step by Step
$z=2[cos\frac{\pi}{6}+isin\frac{\pi}{6}]$
and
$w=2[cos\frac{\pi}{3}+isin\frac{\pi}{3}]$
Calculate $zw$, $\frac{z}{w}$ and $\frac{1}{z}$
$zw=2[cos\frac{\pi}{6}+isin\frac{\pi}{6}]\times 2[cos\frac{\pi}{3}+isin\frac{\pi}{3}]$
$zw=4[cos(\frac{\pi}{6}+\frac{\pi}{3})+i(sin(\frac{\pi}{6}+\frac{\pi}{3})]$
Hence, $zw=4[cos(\frac{\pi}{2})+isin(\frac{\pi}{2})]$
$\frac{z}{w}=\frac{2[cos\frac{\pi}{6}+isin\frac{\pi}{6}]}{2[cos\frac{\pi}{3}+isin\frac{\pi}{3}]}$
$\frac{z}{w}=\frac{2}{2} [cos(\pi /6-\pi/3)+isin(\pi/6-\pi/3)]$
Hence, $\frac{z}{w}=cos(-\pi/6)+isin(-\pi/6)]$
$\frac{1}{z}=\frac{1}{2[cos\frac{\pi}{6}+isin\frac{\pi}{6}]}$
$\frac{1}{z}=\frac{1(cos 0+isin0)}{2[cos\frac{\pi}
{6}+isin\frac{\pi}{6}]}$
Hence, $\frac{1}{z}=\frac{1}{2}[cos(-\frac{\pi}{6})+isin(-\frac{\pi}{6})]$
