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.

If you want a real denominator, you then multiply top and bottom by the complex conjugate (here, $-i$), then work out the result... — abiessu, Jun 12 '17 at 15:32

score 2 · Answer 1 · answered Jun 12 '17 at 15:32

2

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

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

answered Jun 12 '17 at 15:32

Jack

460

score 1 · Accepted Answer · answered Jun 12 '17 at 15:32

1

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

answered Jun 12 '17 at 15:32

Sahiba Arora

10,847

score 0 · Answer 3 · answered Jun 12 '17 at 15:32

0

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

answered Jun 12 '17 at 15:32

PMar

1

score 0 · Answer 4 · answered Jun 13 '17 at 04:55

0

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

answered Jun 13 '17 at 04:55

Χpẘ

1,130
6
8

score 0 · Answer 5 · answered Jun 13 '17 at 04:57

0

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

answered Jun 13 '17 at 04:57

Saketh Malyala

13,637

How to divide a number by $i$

5 Answers5