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

May 18, 2016

$\frac{3 - 2 i}{3 + 2 i} = \frac{5}{13} - \frac{12}{13} i$

#### Explanation:

Given a complex number $a + b i$, the complex conjugate of that number is $a - b i$. 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.

$\frac{3 - 2 i}{3 + 2 i} = \frac{\left(3 - 2 i\right) \left(3 - 2 i\right)}{\left(3 + 2 i\right) \left(3 - 2 i\right)}$

$= \frac{5 - 12 i}{13}$

$= \frac{5}{13} - \frac{12}{13} i$