# How do you simplify (4+2i)/(1-i)?

Feb 5, 2016

$\frac{4 + 2 i}{1 - i} = 1 + 3 i$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \frac{4 + 2 i}{1 - i}$

Multiply numerator and denominator by the complex conjugate of the denominator
$\textcolor{w h i t e}{\text{XXX}} \frac{4 + 2 i}{1 - i} \times \frac{1 + i}{1 + i}$

color(white)("XXX")=(4+2i+4i+2i^2)/(1-i^2

$\textcolor{w h i t e}{\text{XXX}} = \frac{4 + 6 i - 2}{1 - \left(- 1\right)}$

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

$\textcolor{w h i t e}{\text{XXX}} = 1 + 3 i$