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

Dec 13, 2015

$i$

#### Explanation:

Multiply by the complex conjugate of the denominator.

$\frac{2 + 3 i}{3 - 2 i} \left(\frac{3 + 2 i}{3 + 2 i}\right) = \frac{6 + 13 i + 6 {i}^{2}}{9 - 4 {i}^{2}}$

Recall that since $i = \sqrt{- 1}$, it's true that ${i}^{2} = - 1$.

$= \frac{6 + 13 i + 6 \left(- 1\right)}{9 - 4 \left(- 1\right)} = \frac{13 i}{13} = i$