Question

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

Answer 1

`5/2-1/2i`

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

`(3+3i-2i-2i^2)/(1^2-i^2)` and now using `i^2=-1`, this becomes

`(5-i)/2` or `5/2-1/2i`