# How do you simplify (4+2i)/(3-i)?

May 28, 2016

Multiply by the conjugate of the denominator to find that
$\frac{4 + 2 i}{3 - i} = 1 + i$

#### 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 a complex number and its conjugate will be a real number. We will use that to eliminate the complex number from the denominator.

$\frac{4 + 2 i}{3 - i} = \frac{\left(4 + 2 i\right) \left(3 + i\right)}{\left(3 - i\right) \left(3 + i\right)}$

$= \frac{10 + 10 i}{10}$

$= 1 + i$