# How do you divide ( 1+6i)/(4+2i)?

Jan 29, 2016

$\frac{1 + 6 i}{4 + 2 i} = \frac{4}{5} + \frac{11}{10} i$

#### Explanation:

The conjugate of a complex number $a + b i$ is $a - b i$. Using the fact that the product of a complex number and its conjugate is a real number, we can simply the given expression by multiplying the numerator and denominator by the conjugate of the denominator.

$\frac{1 + 6 i}{4 + 2 i} = \frac{\left(1 + 6 i\right) \left(4 - 2 i\right)}{\left(4 + 2 i\right) \left(4 - 2 i\right)}$

$= \frac{4 + 24 i - 2 i + 12}{16 + 8 i - 8 i + 4}$

$= \frac{16 + 22 i}{20}$

$= \frac{4}{5} + \frac{11}{10} i$