# How do you divide (-7+6i)/(7-10i)?

Dec 1, 2016

$- \frac{109}{149} - \frac{28}{149} i$

#### Explanation:

You can multiply both the terms of the fraction by the same expression $7 + 10 i$ to get:

$\frac{\left(- 7 + 6 i\right) \left(7 + 10 i\right)}{\left(7 - 10 i\right) \left(7 + 10 i\right)}$

$= \frac{- 49 - 70 i + 42 i + 60 {i}^{2}}{49 - 100 {i}^{2}}$

Then, since ${i}^{2} = - 1$, you get

$= \frac{- 49 - 28 i - 60}{49 + 100}$

$= \frac{- 28 i - 109}{149}$

that's, in standard form:

$= - \frac{109}{149} - \frac{28}{149} i$