# How do you divide  (1+7i) / (9-5i)  in trigonometric form?

##### 1 Answer
Jun 4, 2016

The result of division is $\frac{1}{53} \left(- 13 + 34 i\right)$
Its trignometrical form $\frac{\sqrt{1325}}{53} \left(- \frac{13}{\sqrt{1325}} + \frac{34}{\sqrt{1325}} i\right)$

#### Explanation:

First of all multiply the numerator and the denominator by the conjugate of denominator.

$\frac{\left(1 + 7 i\right) \left(9 + 5 i\right)}{\left(9 - 5 i\right) \left(9 + 5 i\right)} = \frac{- 26 + 68 i}{106}$

=$\frac{1}{53} \left(- 13 + 34 i\right)$

Now Modulus would be $\sqrt{{13}^{2} + {34}^{2}} = \sqrt{1325}$

The number can now be written as $\frac{\sqrt{1325}}{53} \left(- \frac{13}{\sqrt{1325}} + \frac{34}{\sqrt{1325}} i\right)$

The number now is in trignometrical form its Modulus is $\frac{\sqrt{1325}}{53}$ and arg is ${\tan}^{-} 1 \left(\frac{34}{- 13}\right)$