# How do you divide (-2-10i)/(9-9i)?

Jan 12, 2017

The answer is $= \frac{4}{9} - \frac{2}{3} i$

#### Explanation:

If $z = a + i b$

Then, $\overline{z} = a - i b$

$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

${i}^{2} = - 1$

To simplify the denominator of the quotient of 2 complex numbers, multiply numerator and denominator by the conjugate of the denominator

$\frac{- 2 - 10 i}{9 - 9 i}$

$= \frac{\left(- 2 - 10 i\right) \left(9 + 9 i\right)}{\left(9 - 9 i\right) \left(9 + 9 i\right)}$

$= \frac{- 18 - 18 i - 90 i - 90 {i}^{2}}{81 - 81 {i}^{2}}$

$= \frac{- 18 - 108 i + 90}{81 + 81}$

$= \frac{72 - 108 i}{162}$

$= \frac{36 - 54 i}{81}$

$= \frac{4 - 6 i}{9}$

$= \frac{4}{9} - \frac{2}{3} i$