Question

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

Answer 1

`5/2+1/2i`

Explanation:

Multiply by the complex conjugate of the denominator.

`(3-2i)/(1-i)((1+i)/(1+i))=(3+i-2i^2)/(1-i^2)`

Since `i=sqrt(-1)`, it's also true that `i^2=-1`.

`=(3+i-2(-1))/(1-(-1))=(5+i)/2=5/2+1/2i`

Note that the answer is written in the `a+bi` form of a complex number.