# How do you simplify 20(cos((7pi)/6)+isin((7pi)/6))div15(cos((11pi)/3)+isin((11pi)/3)) and express the result in rectangular form?

Jan 17, 2017

$= - \frac{4}{3} i$

#### Explanation:

In polar complex, that's:

$\frac{20 {e}^{i \frac{7 \pi}{6}}}{15 {e}^{i \frac{11 \pi}{3}}}$

$= \frac{4}{3} {e}^{- \frac{5 \pi}{2}}$

$= \frac{4}{3} {e}^{- \frac{\pi}{2}}$

$= - \frac{4 i}{3}$