Answer
$z_{1}z_{2}=\displaystyle \cos\frac{13\pi}{12}+i\sin\frac{13\pi}{12}$
$\displaystyle \frac{z_{1}}{z_{2}}=\cos\frac{5\pi}{12}+i\sin\frac{5\pi}{12}$
Work Step by Step
See p. 605,
If the two complex numbers $z_{1}$ and $z_{2}$ have the polar forms
If $z_{1}=r_{1}(\cos\theta_{1}+i\sin\theta_{1})$,
$z_{2}=r_{2}(\cos\theta_{2}+i\sin\theta_{2})$, then
$z_{1}z_{2}=r_{1}r_{2}[\cos(\theta_{1}+\theta_{2})+i\sin(\theta_{1}+\theta_{2})]$
$\displaystyle \frac{z_{1}}{z_{2}}=\frac{r_{1}}{r_{2}}[\cos(\theta_{1}-\theta_{2})+i\sin(\theta_{1}-\theta_{2})],\quad z_{2}\neq 0$
----------
$r_{1}r_{2}=1\cdot 1=1,$
$\displaystyle \frac{3\pi}{4}+\frac{\pi}{3}=\frac{(9+4)\pi}{12}=\frac{13\pi}{12},$
$ \displaystyle \frac{r_{1}}{r_{2}}=\frac{1}{1}=1$
$\displaystyle \frac{3\pi}{4}-\frac{\pi}{3}=\frac{(9-4)\pi}{12}=\frac{5\pi}{12},$
$z_{1}z_{2}=\displaystyle \cos\frac{13\pi}{12}+i\sin\frac{13\pi}{12}$
$\displaystyle \frac{z_{1}}{z_{2}}=\cos\frac{5\pi}{12}+i\sin\frac{5\pi}{12}$
