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

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SUMMARY

The discussion confirms that -i is indeed equal to 1/i in the context of complex numbers. Participants demonstrated this by multiplying both sides of the equation, resulting in 1. The simplification of 1/i to -i was also explored through alternative expressions, such as i^3/i^4. Overall, the conversation highlights the importance of understanding the properties of imaginary numbers in mathematics.

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  • Understanding of complex numbers and their properties
  • Familiarity with basic algebraic manipulation
  • Knowledge of the imaginary unit 'i'
  • Experience with mathematical expressions and simplifications
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  • Learn about the geometric interpretation of complex numbers
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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
 
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No, it equals 5...

J/k, yes -i = 1/i:smile:
 
some_dude said:
No, it equals 5...

J/k, yes -i = 1/i:smile:

Phew, thank you!

I thought for a second I'd broken maths...
 
I also thought you... broke him
 
Another approach is to express 1/i as i^3/i^4.
This simplifies to -i/1
 
trister said:
Please help, it's been bugging me and google didn't give any answers
Ha, have you tried googling "1/i" ? :D
 
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...
 
I wonder what the B(1/i)ng search engine would give...
 
Bing interpreted "1/i" as "1 i" and gave a lot of non-math websites- stick to google!
 

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