# How do you simplify (-6-8i)/(4+12i) ?

Feb 12, 2016

#### Answer:

$\frac{- 3 + i}{4}$

#### Explanation:

We will multiply the numerator and the denominator by something called a "complex conjugate." It is the opposite of the current denominator.

So, $4 - 12 i$ is our conjugate.

This leads to $\frac{- 6 - 8 i}{4 + 12 i}$* $\frac{4 - 12 i}{4 - 12 i}$

Foil the numerators to get $- 24 + 72 i - 32 i + 96 {i}^{2}$

Foil the denominators to get $16 - 48 i + 48 i - 144 {i}^{2}$

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

Now, the numerator becomes $- 24 + 40 i + 96 \left(- 1\right)$
---> $- 24 - 96 + 40 i$
---> $- 120 + 40 i$

The denominator becomes $16 - 144 \left(- 1\right)$
--->$16 + 144$
---> $160$

No we have $\frac{- 120 + 40 i}{160}$

Reducing we get $\frac{- 3 + i}{4}$