# Is -i = 1/i ?

1. Jun 17, 2010

### trister

Maybe this is something that's well known but I'd never heard of before, or maybe it's simply incorrect, but is negative i equal to the reciprocal of i?

-i = 1/i

My reasoning being that multiplying both sides of the equation gives 1.

LHS: -i * i = -(-1) = 1
RHS: i/i = 1

2. Jun 17, 2010

### some_dude

No, it equals 5...

J/k, yes -i = 1/i

3. Jun 17, 2010

### trister

Phew, thank you!

I thought for a second I'd broken maths...

4. Jun 17, 2010

### Mentallic

I also thought you... broke him

5. Jun 17, 2010

### The Chaz

Another approach is to express 1/i as i^3/i^4.
This simplifies to -i/1

6. Jun 17, 2010

### Gerenuk

Ha, have you tried googling "1/i" ? :D

7. Jun 17, 2010

### Office_Shredder

Staff Emeritus

I can't believe that's not the first thing you tried!

EDIT: Actually googling 1/i gives a result in google calculator....

8. Jun 17, 2010

### The Chaz

I wonder what the B(1/i)ng search engine would give...

9. Jun 17, 2010

### HallsofIvy

Staff Emeritus
Bing interpreted "1/i" as "1 i" and gave a lot of non-math websites- stick to google!