# How do you simplify 9/(7+i)?

Jan 13, 2016

$\frac{9}{7 + i} = \frac{63 - 9 i}{50} = \frac{63}{50} - \frac{9}{50} i$

#### Explanation:

1. Find the complex coniugate of denominator

denominator: $z = 7 + i$

denominator complex coniugate: $\overline{z} = 7 \textcolor{red}{-} i$

1. Multiply both numerator and denominator for the complex coniugate

$\frac{9}{7 + i} \cdot \frac{7 - i}{7 - i} = \frac{63 - 9 i}{{7}^{2} - {\left(i\right)}^{2}} =$

Remembering that: ${i}^{2} = - 1$

$= \frac{63 - 9 i}{49 - \left(- 1\right)} = \frac{63 - 9 i}{49 + 1} = \frac{63 - 9 i}{50} = \frac{63}{50} - \frac{9}{50} i$