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

Dec 22, 2015

$\frac{6 + i}{6 - i} = \frac{35 + 12 i}{37}$
$\textcolor{w h i t e}{\text{XXXXXXXXXXXX}}$(although I'm not sure this is "simpler")

#### Explanation:

We can clear the complex number from the denominator by multiplying by the complex conjugate.

$\frac{6 + i}{6 - i} \times \frac{6 + i}{6 + i}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{36 + 12 i + {i}^{2}}{36 - {i}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{35 + 12 i}{37}$