Is -i Equal to 1/i in Complex Numbers?

[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

Please help, it's been bugging me and google didn't give any answers

 

[some_dude]

No, it equals 5...

J/k, yes -i = 1/i

 

[trister]

No, it equals 5...

J/k, yes -i = 1/i

Phew, thank you!

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

 

[Mentallic]

I also thought you... broke him

 

[The Chaz]

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

 

[Gerenuk]

Please help, it's been bugging me and google didn't give any answers

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

 

[Office_Shredder]

You had to google 'Reciprocal of the imaginary unit'

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

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

 

[The Chaz]

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

 

[HallsofIvy]

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