# How do you simplify (7+4i)/(2-3i)?

Aug 12, 2016

$\frac{2}{13} + \frac{29}{13} i$

#### Explanation:

To simplify this fraction we have to make the denominator real.

To do this multiply the numerator and denominator by the $\textcolor{b l u e}{\text{complex conjugate}}$ of 2 - 3i

The conjugate of 2 - 3i is 2 + 3i

Note that $\left(2 - 3 i\right) \left(2 + 3 i\right) = 13 \text{ a real number}$

Multiply numerator/denominator by 2 + 3i

$\frac{\left(7 + 4 i\right) \left(2 + 3 i\right)}{\left(2 - 3 i\right) \left(2 + 3 i\right)} = \frac{14 + 29 i + 12 {i}^{2}}{13} = \frac{2 + 29 i}{13}$

$\Rightarrow \frac{7 + 4 i}{2 - 3 i} = \frac{2}{13} + \frac{29}{13} i$