How to divide a number by $i$

Question

I was wondering how to divide a number by $i=\sqrt{-1}$. E.g $$\frac{2}{i} = \ ?$$ Any help would be appreciated.

Answer 1

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

Answer 2

Dividing by $i$ is equivalent to multiplying by -$i$.

Answer 3

It is the same as multiplication by $-i$:

$\frac{a}{i} = \frac{a}{i} \cdot \frac{i}{i} = -i a$

Answer 4

You could start with a known identity and then work you way backwards to the problem in the OP. For example $i^2=-1 \Rightarrow i=\frac{-1}i \Rightarrow -2\cdot i = -2 \cdot \frac{-1}i \Rightarrow -2i=\frac2i$

Answer 5

$\displaystyle \frac{2}{i} \times \frac{i}{i}=\frac{2i}{-1}=-2i$