# How do you divide (3 + 2i) / (2 - 6i)?

Mar 28, 2016

You must multiply the whole expression by the conjugate of the denominator, just like you did when you were younger when you were to rationalize the denominator.

#### Explanation:

The conjugate forms a difference of squares. Therefore, to find it, you must switch the sign in the middle.

Thus, the conjugate is $2 + 6 i$

$\frac{3 + 2 i}{2 - 6 i} \times \frac{2 + 6 i}{2 + 6 i}$

Now multiply. Don't forget that ${i}^{2} = - 1$

(6 + 4i + 12i - 12)/(4 - (36 xx -1)

Don't forget that you can combine $i$'s with $i$'s but you cannot combine non $i ' s$ with $i ' s$.

$\frac{6 + 16 i - 12}{40}$

$\frac{- 6 + 16 i}{40}$

This is as simplified as possible.

Practice exercises:

1. Evaluate:

a). $\frac{4 + 2 i}{3 - 5 i}$

b). $\frac{4 x + 3 i}{- x + 2 i}$

Good luck!