# How do you divide (-5-3i) -: (7-10i)?

Jul 6, 2018

$\frac{- 5 - 3 i}{7 - 10 i} = - \frac{5}{149} - \frac{71}{149} i$

#### Explanation:

We can multiply both numerator and denominator by the complex conjugate $7 + 10 i$ as follows:

$\frac{- 5 - 3 i}{7 - 10 i} = \frac{\left(- 5 - 3 i\right) \left(7 + 10 i\right)}{\left(7 - 10 i\right) \left(7 + 10 i\right)}$

$\textcolor{w h i t e}{\frac{- 5 - 3 i}{7 - 10 i}} = \frac{\left(- 5\right) \left(7\right) + \left(- 5\right) \left(10 i\right) + \left(- 3 i\right) \left(7\right) + \left(- 3 i\right) \left(10 i\right)}{{\left(7\right)}^{2} - {\left(10 i\right)}^{2}}$

$\textcolor{w h i t e}{\frac{- 5 - 3 i}{7 - 10 i}} = \frac{- 35 - 50 i - 21 i + 30}{49 + 100}$

$\textcolor{w h i t e}{\frac{- 5 - 3 i}{7 - 10 i}} = \frac{- 5 - 71 i}{149}$

$\textcolor{w h i t e}{\frac{- 5 - 3 i}{7 - 10 i}} = - \frac{5}{149} - \frac{71}{149} i$