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

Feb 18, 2017

$- \frac{12}{13} - \frac{5}{13} i$

#### Explanation:

Use the conjugate of the denominator to multiply by one:
$\frac{2 + 3 i}{- 3 - 2 i} = \frac{2 + 3 i}{- 3 - 2 i} \cdot \frac{- 3 + 2 i}{- 3 + 2 i} = \frac{- 6 + 4 i - 9 i + 6 {i}^{2}}{9 - 4 {i}^{2}}$

Remember that ${i}^{2} = - 1$

Simplify and combine like-terms :
$\frac{- 6 + 4 i - 9 i - 6}{9 + 4} = \frac{- 12 - 5 i}{13} = - \frac{12}{13} - \frac{5}{13} i$