# What does (1+3i)/(2+2i) equal in a+bi form?

Oct 21, 2015

#### Answer:

I found: $1 + \frac{1}{2} i$

#### Explanation:

First multiply and divide by the complex conjugate of the denominator to get a Pure Real denominator:
$\frac{1 + 3 i}{2 + 2 i} \cdot \textcolor{red}{\frac{2 - 2 i}{2 - 2 i}} =$
$= \frac{\left(1 + 3 i\right) \left(2 - 2 i\right)}{4 + 4} = \frac{2 - 2 i + 6 i - 6 {i}^{2}}{8} =$
but ${i}^{2} = - 1$
$\frac{8 + 4 i}{8} = \frac{8}{8} + \frac{4}{8} i = 1 + \frac{1}{2} i$