# How do you divide (-4+3i)/(-10+7i)?

Aug 1, 2016

$\frac{61}{149} - \frac{2}{149} i$

#### Explanation:

Since $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2} \mathmr{and} {i}^{2} = - 1$

you can multiply numerator and denominator of the fraction by $+ 10 + 7 i$ and have:

$\frac{\left(- 4 + 3 i\right) \left(10 + 7 i\right)}{\left(- 10 + 7 i\right) \left(10 + 7 i\right)} =$

$\frac{- 40 - 28 i + 30 i + 21 {i}^{2}}{- 100 + 49 {i}^{2}} =$

$\frac{- 40 + 2 i - 21}{- 100 - 49} =$

$\frac{- 61 + 2 i}{-} 149 =$

$\frac{61}{149} - \frac{2}{149} i$ in standard form