# How do you simplify (3-2i)/(1-i)?

Dec 13, 2015

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

#### Explanation:

Multiply by the complex conjugate of the denominator.

$\frac{3 - 2 i}{1 - i} \left(\frac{1 + i}{1 + i}\right) = \frac{3 + i - 2 {i}^{2}}{1 - {i}^{2}}$

Since $i = \sqrt{- 1}$, it's also true that ${i}^{2} = - 1$.

$= \frac{3 + i - 2 \left(- 1\right)}{1 - \left(- 1\right)} = \frac{5 + i}{2} = \frac{5}{2} + \frac{1}{2} i$

Note that the answer is written in the $a + b i$ form of a complex number.