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Is -i = 1/i ?

  1. Jun 17, 2010 #1
    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
  2. jcsd
  3. Jun 17, 2010 #2
    No, it equals 5...

    J/k, yes -i = 1/i:smile:
  4. Jun 17, 2010 #3
    Phew, thank you!

    I thought for a second I'd broken maths...
  5. Jun 17, 2010 #4


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    I also thought you... broke him
  6. Jun 17, 2010 #5
    Another approach is to express 1/i as i^3/i^4.
    This simplifies to -i/1
  7. Jun 17, 2010 #6
    Ha, have you tried googling "1/i" ? :D
  8. Jun 17, 2010 #7


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    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....
  9. Jun 17, 2010 #8
    I wonder what the B(1/i)ng search engine would give...
  10. Jun 17, 2010 #9


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