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

  • Context: High School 
  • Thread starter Thread starter trister
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Discussion Overview

The discussion revolves around the equality of -i and 1/i in the context of complex numbers. Participants explore this relationship through various reasoning and expressions, including mathematical manipulations and informal commentary.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes that -i equals 1/i, reasoning that multiplying both sides results in 1.
  • Another participant humorously affirms the equality, suggesting that the initial claim is correct.
  • A different approach is presented, expressing 1/i as i^3/i^4, which simplifies to -i/1.
  • Several participants engage in light-hearted banter regarding the search for information on this topic, indicating a lack of initial clarity on the subject.

Areas of Agreement / Disagreement

While some participants humorously affirm the equality of -i and 1/i, there is no formal consensus reached on the mathematical validity of the claim, and the discussion includes playful exchanges rather than a rigorous debate.

Contextual Notes

Some participants express uncertainty about the initial claim and the effectiveness of search engines in providing relevant information on the topic.

Who May Find This Useful

Readers interested in complex numbers, mathematical reasoning, or informal discussions about mathematical concepts may find this thread engaging.

trister
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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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