# How do you simplify (4+9i)/(2+6i)?

Apr 5, 2018

$\frac{31 - 3 i}{20}$

#### Explanation:

Start by multiplying both the numerator and the denominator by the conjugate of the denominator:

$\left(\frac{4 + 9 i}{2 + 6 i}\right) \left(\frac{2 - 6 i}{2 - 6 i}\right) =$

Use the distributive property to get back to a single fraction:

$\frac{8 - 6 i - 54 {i}^{2}}{4 - 36 {i}^{2}} =$

Convert ${i}^{2}$ to $- 1$ and combine like terms:

$\frac{62 - 6 i}{40} =$

Reduce to lowest terms:

$\frac{31 - 3 i}{20}$