# How do you divide ( -7i-3) / ( 9 i -4 ) in trigonometric form?

May 22, 2017

$\frac{\sqrt{5626}}{97} \cdot c i s \left({132.84}^{o}\right) = - \frac{51}{97} + \frac{55}{97} \cdot i$

#### Explanation:

To evaluate the division in trig. Form, first you convert the numerator and denominator to polar form:
The numerator in polar form: $- 7 \cdot i - 3 = \sqrt{58} \cdot c i s \left(- {113.20}^{o}\right)$
The denominator in polar form: $9 \cdot i - 4 = \sqrt{97} \cdot c i s \left({113.96}^{o}\right)$

Then evaluate the division:
$\frac{- 7 i - 3}{9 i - 4}$
$= \left(\frac{\sqrt{58}}{\sqrt{97}}\right) \cdot c i s \left(- {113.20}^{o} - {113.96}^{o}\right)$
$= \frac{\sqrt{5626}}{97} \cdot c i s \left({132.84}^{o}\right)$

Convert back to rectangular form:
$= - \frac{51}{97} + \frac{55}{97} \cdot i$