Question

How do you divide `(3 + 2i) / (2 - 6i)`?

Answer 1

You must multiply the whole expression by the conjugate of the denominator, just like you did when you were younger when you were to rationalize the denominator.

Explanation:

The conjugate forms a difference of squares. Therefore, to find it, you must switch the sign in the middle.

Thus, the conjugate is `2 + 6i`

`(3 + 2i)/(2 - 6i) xx (2 + 6i)/(2 + 6i)`

Now multiply. Don't forget that `i^2 = -1`

`(6 + 4i + 12i - 12)/(4 - (36 xx -1)`

Don't forget that you can combine `i`'s with `i`'s but you cannot combine non `i's` with `i's`.

`(6 + 16i - 12)/40`

`(-6 + 16i)/40`

This is as simplified as possible.

Practice exercises:

1. Evaluate:

a). `(4 + 2i)/(3 - 5i)`

b). `(4x + 3i)/(-x + 2i)`

Good luck!