# How do you divide 5/(1+i)?

Jan 9, 2016

I found $2.5 - 2.5 i$

#### Explanation:

Multiply and divide by the complex conjugate of the denominator:
$\frac{5}{1 + i} \cdot \textcolor{red}{\frac{1 - i}{1 - i}} = \frac{5 - 5 i}{1 - i + i - {i}^{2}} =$
Where ${i}^{2} = - 1$:

$= \frac{5 - 5 i}{2} = \frac{5}{2} - \frac{5}{2} i =$

$= 2.5 - 2.5 i$