Question

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

Answer 1

`i`

Explanation:

Multiply by the complex conjugate of the denominator.

`(2+3i)/(3-2i)((3+2i)/(3+2i))=(6+13i+6i^2)/(9-4i^2)`

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

`=(6+13i+6(-1))/(9-4(-1))=(13i)/13=i`