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What's wrong with these equations?

  1. Jan 29, 2009 #1
    1=2? -1=1?

    Code (Text):




    Code (Text):




    1/i=i/1 note: i=sqrt(-1) complex number

    i/(i^2)=i note: i/(i^2) equals 1/i as in 3/9 equals 1/3

    i/-1=i note: i^2=-1 complex number


    i*(-i)=i*(i) note: preserved equality of equation

  2. jcsd
  3. Jan 29, 2009 #2
    The error of your first example is that devision by zero is undefined, [tex]1-1=0[/tex].

    The second example fails duo to use of the identity [tex]\sqrt{\frac ab}=\frac{\sqrt a}{\sqrt b}[/tex], since this is only valid for [tex]a,b>0[/tex]. See http://en.wikipedia.org/wiki/Exponentiation#Failure_of_power_and_logarithm_identities", for more info.

    See more similar "proofs" http://en.wikipedia.org/wiki/Invalid_proof" [Broken].
    Last edited by a moderator: May 3, 2017
  4. Jan 29, 2009 #3
    Now that was simple, thank you. I saw this around and it was messing with me. Guess math can't be tricked. Never would have guessed something similar was already on wikipedia. Thank you!
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