# How do you divide (4+i)/(8+9i)?

Dec 18, 2016

$\frac{41}{145} - \frac{28}{145} i$

#### Explanation:

To divide the fraction we multiply the numerator/denominator by the $\textcolor{b l u e}{\text{complex conjugate}}$ of the denominator.

$8 + 9 i \text{ has conjugate } 8 - 9 i$

$\Rightarrow \frac{4 + i}{8 + 9 i} = \frac{\left(4 + i\right) \left(8 - 9 i\right)}{\left(8 + 9 i\right) \left(8 - 9 i\right)}$

expand numerator/denominator using FOIL method.

$= \frac{32 - 36 i + 8 i - 9 {i}^{2}}{64 - 72 i + 72 i - 81 {i}^{2}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} {i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1$

$= \frac{41 - 28 i}{145} = \frac{41}{145} - \frac{28}{145} i$