# How do you simplify (-3 + 2i) / (2 - 5i)?

Jun 30, 2016

$\frac{- 3 + 2 i}{2 - 5 i} = - \frac{16}{29} - \frac{11}{29} i$

#### Explanation:

To simplify $\frac{- 3 + 2 i}{2 - 5 i}$, we need to multiply numerator and denominator by complex conjugate of the denominator i.e. here $2 + 5 i$.

Hence, $\frac{- 3 + 2 i}{2 - 5 i} = \frac{\left(- 3 + 2 i\right) \left(2 + 5 i\right)}{\left(2 - 5 i\right) \left(2 + 5 i\right)}$

= $\frac{- 6 - 15 i + 4 i + 10 {i}^{2}}{4 - 25 {i}^{2}}$

= $\frac{- 6 - 15 i + 4 i - 10}{4 + 25}$

= $\frac{- 16 - 11 i}{29} = - \frac{16}{29} - \frac{11}{29} i$