# How do you divide (-1+5i)/(-8-7i)?

$\frac{- 1 + 5 i}{- 8 - 7 i} = - \frac{27}{113} - \frac{47 i}{113}$

#### Explanation:

To do the division, we have to make use of the conjugate of the complex number at the numerator and denominator. The conjugate of $- 8 - 7 i$ is $- 8 + 7 i$

$\frac{- 1 + 5 i}{- 8 - 7 i} = \frac{- 1 + 5 i}{- 8 - 7 i} \cdot \frac{- 8 + 7 i}{- 8 + 7 i}$

$\frac{- 1 + 5 i}{- 8 - 7 i} = \frac{- 1 \cdot \left(- 8 + 7 i\right) + 5 i \cdot \left(- 8 + 7 i\right)}{64 + 49}$

$\frac{- 1 + 5 i}{- 8 - 7 i} = \frac{+ 8 - 7 i - 40 i - 35}{64 + 49}$

$\frac{- 1 + 5 i}{- 8 - 7 i} = \frac{- 27 - 47 i}{113}$

$\frac{- 1 + 5 i}{- 8 - 7 i} = - \frac{27}{113} - \frac{47 i}{113}$

God bless....I hope the explanation is useful.