# How do you simplify (3-2i)/(1- i) and write in a+bi form?

##### 1 Answer
Feb 26, 2016

$\frac{5}{2} - \frac{1}{2} i$

#### Explanation:

To simplify (3−2i)/(1−i) and write in a+bi form

we need to multiply and divide the fraction by denominator's complex conjugate i.e. $1 + i$. The fraction then becomes

((3−2i)(1+i))/((1−i)(1+i) or

$\frac{3 + 3 i - 2 i - 2 {i}^{2}}{{1}^{2} - {i}^{2}}$ and now using ${i}^{2} = - 1$, this becomes

$\frac{5 - i}{2}$ or $\frac{5}{2} - \frac{1}{2} i$