# How do you simplify (1+3i )/( 2+2i)?

Nov 29, 2015

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

#### Explanation:

You need to change the denominator into a pure real number by multiplying and dividing by the complex conjugate of the denominator:
$\frac{1 + 3 i}{2 + 2 i} \cdot \frac{2 - 2 i}{2 - 2 i} =$ multiply :
$= \frac{2 - 2 i + 6 i - 6 {i}^{2}}{4 + 4} =$
considering that: ${i}^{2} = - 1$:
$= \frac{2 + 4 i + 6}{8} =$
$= \frac{8 + 4 i}{8} =$
$= 4 \frac{2 + i}{8} =$
$= \frac{2 + i}{2} = 1 + \frac{1}{2} i$