# How do you divide -2/i?

Oct 24, 2016

#### Answer:

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

#### Explanation:

$i$ is a complex number so we can't directly divide by it.

however, we can rationalise the denominator to find another war of expressing it.

$i$ can be written as $\sqrt{- 1}$

so we have,

$\frac{- 2}{\sqrt{- 1}}$

$= \frac{- 2}{\sqrt{- 1}} \cdot 1$

$= \frac{- 2}{\sqrt{- 1}} \cdot \frac{\sqrt{- 1}}{\sqrt{- 1}}$ (multiplying by 1 doesn't change the number)

$= \frac{- 2 \cdot \sqrt{- 1}}{\sqrt{- 1} \cdot \sqrt{- 1}}$

$= \frac{- 2 \cdot \sqrt{- 1}}{-} 1$

$= 2 \cdot \sqrt{- 1}$

$= 2 i$

so,

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

unfortunately, we can determine an actual number as $i$ is complex.

Hope this helped.