# How do you divide (-3-2i)/(-10-3i)?

Dec 2, 2016

The answer is $= \frac{36}{109} + \frac{11}{109} i$

#### Explanation:

We multiply numerator and denominator by the conjugate of the denominator.

If $z = a + i b$

The conjugate is $\overline{z} = a - i b$

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

So,

$\frac{- 3 - 2 i}{- 10 - 3 i} = \frac{\left(- 3 - 2 i\right) \left(- 10 + 3 i\right)}{\left(- 10 - 3 i\right) \left(- 10 + 3 i\right)}$

$= \frac{30 - 9 i + 20 i - 6 {i}^{2}}{100 - 9 {i}^{2}}$

$= \frac{36 + 11 i}{109}$

$= \frac{36}{109} + \frac{11}{109} i$