# What does (3+7i)/(12+5i) equal in a+bi form?

Oct 23, 2015

$\frac{3 + 7 i}{12 + 5 i} = \frac{71}{169} + \frac{69}{169} i$

#### Explanation:

Multiply numerator and denominator by the conjugate of the denominator as follows:

$\frac{3 + 7 i}{12 + 5 i} = \frac{\left(3 + 7 i\right) \left(12 - 5 i\right)}{\left(12 + 5 i\right) \left(12 - 5 i\right)}$

$= \frac{36 - 15 i + 84 i - 35 {i}^{2}}{{12}^{2} - {5}^{2} {i}^{2}}$

$= \frac{\left(36 + 35\right) + \left(84 - 15\right) i}{144 + 25}$

$= \frac{71 + 69 i}{169}$

$= \frac{71}{169} + \frac{69}{169} i$