# How do you simplify 20 / (3+i)?

Dec 16, 2015

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

$\frac{20}{3 + i} = 6 - 2 i$

#### Explanation:

$\frac{20}{3 + i}$

$= \frac{20 \left(3 - i\right)}{\left(3 + i\right) \left(3 - i\right)}$

$= \frac{20 \left(3 - i\right)}{{3}^{2} + 1}$

$= \frac{20 \left(3 - i\right)}{10}$

$= 6 - 2 i$