# How do you divide (1+2i)/(2-3i)?

Jan 8, 2016

$\frac{7 i - 4}{13}$

#### Explanation:

The complex conjugate of $2 - 3 i$ is $2 + 3 i$.

$\frac{1 + 2 i}{2 - 3 i} = \frac{1 + 2 i}{2 - 3 i} \cdot \frac{2 + 3 i}{2 + 3 i}$

$= \frac{2 + 6 {i}^{2} + 4 i + 3 i}{{2}^{2} - {\left(3 i\right)}^{2}}$

$= \frac{7 i - 4}{13}$