# How do you divide (-3-9i)/(5-8i)?

Oct 17, 2016

The answer is $\frac{57}{89} - \frac{69 i}{89}$
$\frac{- 3 - 9 i}{5 - 8 i} = \frac{\left(- 3 - 9 i\right) \cdot \left(5 + 8 i\right)}{\left(5 - 8 i\right) \left(5 + 8 i\right)} = \frac{- 15 - 24 i - 45 i - 72 {i}^{2}}{25 - 64 {i}^{2}}$
as ${i}^{2} = - 1$
The result is $\frac{- 15 + 72 - 69 i}{25 + 64} = \frac{57 - 69 i}{89} = \frac{57}{89} - \frac{69 i}{89}$