Posers and Puzzles

Posers and Puzzles

  1. Joined
    04 Aug '01
    Moves
    2408
    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. central usa
    Joined
    22 Jul '03
    Moves
    20848
    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. I'm in Checkmate
    Joined
    11 Mar '04
    Moves
    842
    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. Joined
    26 Apr '03
    Moves
    26583
    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.
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