How do you divide #(3 + 2i) / (2 - 6i)#?
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.
The conjugate forms a difference of squares. Therefore, to find it, you must switch the sign in the middle.
Thus, the conjugate is
Now multiply. Don't forget that
Don't forget that you can combine
This is as simplified as possible.