# Question #dabf9

Jan 26, 2017

The real part is $= \frac{5}{13}$

#### Explanation:

We need

$\left(a - b\right) \left(a + b\right) = {a}^{2} - {b}^{2}$

${i}^{2} = - 1$

The conjugate of $\left(a + i b\right)$ is $\left(a - i b\right)$

We multiply numerator and denominator by the conjugate of the denominator

$\frac{\left(4 - i\right) \left(2 - 3 i\right)}{\left(2 + 3 i\right) \left(2 - 3 i\right)} = \frac{8 - 12 i - 2 i + 3 {i}^{2}}{4 - 9 {i}^{2}}$

$= \frac{5 - 14 i}{13}$

$= \frac{5}{13} - \frac{14}{13} i$

The real part is $= \frac{5}{13}$