# How do you divide (-5-9i)/(9+8i)?

Nov 13, 2016

$\frac{13}{5} - \frac{41}{145} i$

#### Explanation:

You can multiply the terms of the fraction by the same expression:

$9 - 8 i$

to get a denominator without i:

$\frac{\left(- 5 - 9 i\right) \left(9 - 8 i\right)}{\left(9 + 8 i\right) \left(9 - 8 i\right)}$

$= \frac{- 45 + 40 i - 81 i + 72 {i}^{2}}{81 - 64 {i}^{2}}$

$= \frac{- 45 - 41 i - 72}{81 + 64}$ (since ${i}^{2} = - 1$)

$\frac{- 117 - 41 i}{145}$

and, in the standard form:

$- \frac{117}{45} - \frac{41}{145} i$

$= \frac{13}{5} - \frac{41}{145} i$