Question

How do you simplify `5/(2+3i)`?

Answer 1

`10/13-15/13i`

Explanation:

Multiply by the complex conjugate of the bottom.

`5/(2+3i)((2-3i)/(2-3i))=(10-15i)/(4-9i^2)`

Recall that `i=sqrt-1`. Square both sides of that to see that `i^2=-1`.

`=(10-15i)/(4-9(-1))=(10-15i)/13=10/13-15/13i`