# How do you divide ( 4 + 3i) /( 7 + i)?

Jan 26, 2016

$\frac{31}{50} + \frac{17}{50} i$

#### Explanation:

In order to make the denominator not contain complex numbers, multiply the fraction by the complex conjugate of the denominator.

$= \frac{4 + 3 i}{7 + i} \left(\frac{7 - i}{7 - i}\right)$

Distribute each of these.

$= \frac{28 + 17 i - 3 {i}^{2}}{49 - {i}^{2}}$

We can simplify this further, since ${i}^{2} = - 1$.

$= \frac{28 + 17 i - 3 \left(- 1\right)}{49 - \left(- 1\right)}$

$= \frac{28 + 17 i + 3}{49 + 1}$

$= \frac{31 + 17 i}{50}$

Complex numbers are typically written in $a + b i$ form.

$= \frac{31}{50} + \frac{17}{50} i$