# How do you simplify 1/(6-3i)?

Dec 27, 2015

$\frac{1}{6 - 3 i} = \frac{2 + i}{15}$

#### Explanation:

Multiply both the numerator and denominator by the complex conjugate of the denominator:
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{6 - 3 i} \times \frac{6 + 3 i}{6 + 3 i}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{6 + 3 i}{{6}^{2} - {3}^{2} {i}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{6 + 3 i}{36 - \left(9\right) \left(- 1\right)}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{6 + 3 i}{45}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{2 + i}{15}$