# How do you divide (4-2i)/(3+7i)?

Jun 18, 2016

$- \frac{1}{29} - \frac{17}{29} \cdot i$

#### Explanation:

you can multiply numerator and denominator by the expression

$3 - 7 i$

$\frac{\left(4 - 2 i\right) \left(3 - 7 i\right)}{\left(3 + 7 i\right) \left(3 - 7 i\right)}$

and, by symplifying:

$\frac{12 - 28 i - 6 i + 14 {i}^{2}}{9 - 49 {i}^{2}}$

let's substitute ${i}^{2} = - 1$ and sum similar terms:

$\frac{12 - 34 i - 14}{9 + 49}$

$\frac{- 2 - 34 i}{58}$

or

$- \frac{2}{58} - \left(\frac{34}{58}\right) i$

that's

$- \frac{1}{29} - \frac{17}{29} \cdot i$