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

Nov 27, 2015

The result is $1 + i$

#### Explanation:

If you want to calculate a quotient of 2 complex numbers it is good to expand the fraction by the complex conjugate of the denominator to make it (the denominator) a real number:

$\frac{4 + 2 i}{3 - i} = \frac{4 + 2 i}{3 - i} \cdot \frac{3 + i}{3 + i} =$

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

$\frac{10 + 10 i}{10} = \frac{10 \cdot \left(1 + i\right)}{10} = 1 + i$