# How do you divide 6/(-4i)?

Aug 3, 2016

#### Answer:

$\frac{6}{- 4 i} = \frac{3}{2} i$

#### Explanation:

The complex conjugate of a complex number $a + b i$, denoted $\overline{a + b i}$, is given by $\overline{a + b i} = a - b i$. A useful property is that the product of any number and its conjugate is a real number, that is,

$a + b i \cdot \left(\overline{a + b i}\right) \in \mathbb{R}$

We will use that property to remove the complex part from the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

$\frac{6}{- 4 i} = \frac{6 \cdot \left(\overline{- 4 i}\right)}{- 4 i \cdot \left(\overline{- 4 i}\right)}$

$= \frac{6 \cdot \left(4 i\right)}{- 4 i \cdot \left(4 i\right)}$

$= \frac{24 i}{16}$

$= \frac{3}{2} i$