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Posers and Puzzles

Posers and Puzzles

  1. 13 Mar '04 21:52
    This is for those math people who love complex space:

    i think it is very difficult to conceptualize it, but i^i is actually a real number and is very easy to find using Euler's Formula:

    exp(i*Pi) = -1 = i^2
    => i^i = exp(-Pi/2) = 0.207879......

    i think this is fascinating and would like to be able to understand why this is so....can any of you give me a geometric or any other reason why i^i should be a real number?

    thanks
  2. 14 Mar '04 02:50
    Originally posted by davegage
    This is for those math people who love complex space:

    i think it is very difficult to conceptualize it, but i^i is actually a real number and is very easy to find using Euler's Formula:

    exp(i*Pi) = -1 = i^2
    => i^i = exp(-Pi/2) = 0.207879......
    i knew this also, but haven't seen the proof as to why.
    it is logical, though, since i is such an unusual quantity.
    hope soemone else can help us here.
  3. 14 Mar '04 04:25
    It's something I've always just taken for granted. Never eally thought about it, but now I'm curious. Anybody able to elucidate?
  4. 14 Mar '04 18:15
    Originally posted by davegage
    This is for those math people who love complex space:

    i think it is very difficult to conceptualize it, but i^i is actually a real number and is very easy to find using Euler's Formula:

    exp(i*Pi) = -1 = i^2
    => i^i = exp(-Pi/2) = 0.207879......

    i think this is fascinating and would like to be able to understand why this is so....can any of you give me a geometric or any other reason why i^i should be a real number?

    thanks
    Is it because raising a number to an imaginary power rotates it in the complex plane? Raising i to an imaginary power looks like it rotates i exactly onto the real plane.