Question

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

Answer 1

`(3-2i)/(3+2i)=5/13-12/13i`

Explanation:

Given a complex number `a+bi`, the complex conjugate of that number is `a-bi`. A useful property is that the product of any number with its complex conjugate is a real number. We will use that to eliminate the complex number from the denominator.

`(3-2i)/(3+2i) = ((3-2i)(3-2i))/((3+2i)(3-2i))`

`=(5-12i)/13`

`=5/13-12/13i`