Answer
$z_{1}z_{2}=100(\cos 350^{o}+i\sin 350^{o})$
$\displaystyle \frac{z_{1}}{z_{2}}=\frac{4}{25}(\cos 50^{o}+i\sin 50^{o})$
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
$z_{1}z_{2}=r_{1}r_{2}[\cos(\theta_{1}+\theta_{2})+i\sin(\theta_{1}+\theta_{2})]$
$\displaystyle \frac{z_{1}}{z_{2}}=\frac{r_{1}}{r_{2}}[\cos(\theta_{1}-\theta_{2})+i\sin(\theta_{1}-\theta_{2})],\quad z_{2}\neq 0$
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$r_{1}r_{2}=4\cdot 25=100,$
$200^{o}+150^{o}=350^{o}$
$ \displaystyle \frac{r_{1}}{r_{2}}=\frac{4}{25}$
$200^{o}-150^{o}=50^{o}$
$z_{1}z_{2}=100(\cos 350^{o}+i\sin 350^{o})$
$\displaystyle \frac{z_{1}}{z_{2}}=\frac{4}{25}(\cos 50^{o}+i\sin 50^{o})$
