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Math Help - Proof check

  1. #1
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    Proof check

    Not sure where to put this ... I saw this some time ago, but could never really figure out what/where the problem is:

    i=\sqrt{-1}
    i^2=(\sqrt{-1})^2=-1
    \sqrt{-1} \cdot \sqrt{-1}=-1
    \sqrt{(-1) \cdot (-1)}=-1
    \sqrt{1}=-1
    1=-1

    As far as I can tell, the process seems to be valid, but obviously 1 is not -1 ... so what exactly is wrong?
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by Bingk View Post
    Not sure where to put this ... I saw this some time ago, but could never really figure out what/where the problem is:

    i=\sqrt{-1}
    i^2=(\sqrt{-1})^2=-1
    \sqrt{-1} \cdot \sqrt{-1}=-1
    \sqrt{(-1) \cdot (-1)}=-1
    \sqrt{1}=-1
    1=-1

    As far as I can tell, the process seems to be valid, but obviously 1 is not -1 ... so what exactly is wrong?
    The mistake is in third line!
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  3. #3
    MHF Contributor
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    Not all laws of exponentiation extend to complex numbers.

    E.g. a^n\cdot b^n = (a\cdot b)^n is only true for REAL a^n and b^n.
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  4. #4
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    Ah!! Okay ... makes sense ... I feel sort of silly, hehehe. Thanks!
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