# How do you simplify \frac { 8+ 6i } { 3- 2i }?

Dec 2, 2017

$\frac{12 + 34 i}{13}$

#### Explanation:

In order to simplify this, you need to make sure $i$ isn't in the denominator (or bottom) of the fraction. To do this, multiply both the numerator and denominator by the conjugate of $3 - 2 i$, which is $3 + 2 i$. When doing this, make sure to use the FOIL method:

1)

$\frac{\left(8 + 6 i\right) \cdot \left(3 + 2 i\right)}{\left(3 - 2 i\right) \cdot \left(3 + 2 i\right)}$

2)

$\frac{24 + 16 i + 18 i - 12}{9 + 6 i - 6 i - 4 {i}^{2}}$

Since $i$ equals $\sqrt{- 1}$, ${i}^{2}$ equals $- 1$.

3)

$\frac{12 + 34 i}{9 + 4}$

4)

$\frac{12 + 34 i}{13}$