# How do you divide 2/(3 + i)?

Jul 8, 2016

$\frac{2}{3 + i} = \frac{3}{5} - \frac{1}{5} i$

#### Explanation:

Multiply both numerator and denominator by the Complex conjugate $\left(3 - i\right)$ of the denominator and simplify:

$\frac{2}{3 + i} = \frac{2 \left(3 - i\right)}{\left(3 + i\right) \left(3 - i\right)} = \frac{2 \left(3 - i\right)}{{3}^{2} - {i}^{2}} = \frac{2 \left(3 - i\right)}{10} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \left(3 - i\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \cdot 5} = \frac{3}{5} - \frac{1}{5} i$