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

Oct 28, 2016

The answer is $- \frac{12}{13} + \frac{5 i}{13}$

#### Explanation:

To simplify, multiply numerator and denominatorby the conjugate of the denominator
if $z = a + i b$ the the conjugate is $\overline{z} = a - i b$
so the conjugate of the denominator is $3 + 2 i$
and ${i}^{2} = - 1$
Then the expression is $\frac{- 2 + 3 i}{3 - 21} = \frac{\left(- 2 + 3 i\right) \left(3 + 2 i\right)}{\left(3 - 2 i\right) \left(3 + 2 i\right)}$

$= \frac{- 6 - 4 i + 9 i + 6 {i}^{2}}{9 - 4 {i}^{2}} = \frac{- 12 + 5 i}{13} = - \frac{12}{13} + \frac{5 i}{13}$