Question

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

Answer 1

`- 1 - i`

Explanation:

Your denominator is `-2 + i`.

You should take the complex conjugate of the denominator `(-2-i)` and expand your fraction with it:

`(3+i)/(-2+i) = ((3+i) * color(blue)((-2-i)))/((-2+i) * color(blue)((-2-i)))`

`= (-6 -2i - 3i - i^2) / ((-2)^2 - i^2)`

`= (-6 - 5i - i^2)/(4 - i^2)`

... remember that `i^2 = -1`...

`= (-6 - 5i + 1)/(4 + 1)`

`= (-5 - 5i)/5`

`= -5/5 - 5/5 i`

`= - 1 - i`