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I Another negative one equals one proof

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  1. Mar 30, 2017 #1
    Hey guys! I need help proving why this proof is wrong. I know it's wrong, but I can't figure out why. Anyway:
    i = sqrt -1
    i^4 = 1
    1^4 = 1
    Substution: i^4 =1^4
    i = 1
    1 = sqrt -1
    1^2 = -1
    1 = 1^2
    1= -1

    If you have any questions, feel free to ask.
     
  2. jcsd
  3. Mar 30, 2017 #2

    mfb

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    That step is not valid. Just dropping exponents doesn't even work for real numbers.
     
  4. Mar 30, 2017 #3

    fresh_42

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  5. Mar 30, 2017 #4

    Vanadium 50

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    -1^2 = 1^2 therefore -1 = 1. Same idea. Do you see where this fails? No need to drag i into it.
     
  6. Mar 30, 2017 #5
    Yeah, thanks
     
  7. Mar 30, 2017 #6
    4rt them both...
     
  8. Mar 30, 2017 #7

    mfb

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    ##(-1)^4 = 1^4##, but obviously ##-1 \neq 1##.
    This is the one-step version of post 1.
     
  9. Mar 30, 2017 #8

    Mark44

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    But -1^2 ≠ 1^2, as I'm sure you know...

    However, (-1)^2 does equal 1^2.
     
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