# How do you find the quotient of the complex numbers and express your answer in trigonometric form (5(cos(15º) + i sin(15º)))/(3(cos(70º) + i sin(70º)))?

May 16, 2016

$\left(\frac{5}{3}\right) \left(\cos {55}^{o} - i \sin {55}^{o}\right)$.

#### Explanation:

Use ${e}^{\pm i \theta} = \cos \theta \pm i \sin \theta$.

The ratio = $\left(\frac{5}{3}\right) {e}^{i {15}^{o}} / {e}^{i {70}^{o}}$

$= \left(\frac{5}{3}\right) {e}^{i {\left(15 - 70\right)}^{o}}$

$= \left(\frac{5}{3}\right) \left(\cos {55}^{o} - i \sin {55}^{o}\right)$