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

Dec 13, 2015

$\frac{10}{13} - \frac{15}{13} i$

#### Explanation:

Multiply by the complex conjugate of the bottom.

$\frac{5}{2 + 3 i} \left(\frac{2 - 3 i}{2 - 3 i}\right) = \frac{10 - 15 i}{4 - 9 {i}^{2}}$

Recall that $i = \sqrt{-} 1$. Square both sides of that to see that ${i}^{2} = - 1$.

$= \frac{10 - 15 i}{4 - 9 \left(- 1\right)} = \frac{10 - 15 i}{13} = \frac{10}{13} - \frac{15}{13} i$