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Cool thing

  1. Mar 11, 2005 #1
    Just wanted to share a cool thing I found when I was shown Eulers formula...

    e^(pi*i) +1 = 0

    this can be written as

    e^pi = (SQRT -1)ROOT -1

    dont know if I wrote correclty...

    ...........................................................................................
    ...........................................................................................
    ..........#######....########################..........................
    .##....#.......#.........#......................................................................
    ....#.#...--.#........#...................#...............................................
    .....#..........#...... #....................#...............................................
    ........................#..........----...#...................................................
    ..########.....#.......................#......................................................
    .................#...#........................#...............................................
    ..................#.#.........................#..............................................
    ...................#........................................................................
    ...........................................................................................

    Took a time to write this :)


    so can you imagine the number above to equal e^pi which is th real number around 23...? :rofl:
     
  2. jcsd
  3. Mar 11, 2005 #2

    HallsofIvy

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    Science Advisor

    Yes,
    [tex]e^{i\pi}+ 1= 0[/tex]

    (click on that to see the code I used)

    I suspect that just about everyone on this board already knows that- there have been a number of threads about it.
     
  4. Mar 11, 2005 #3
    but is the format i wrote it in also well-known? the cool root stuff I mean...
     
  5. Mar 11, 2005 #4

    shmoe

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    Yes it is. Exponentiation by complex numbers gives some startling results when you first see it.

    Note that [tex]e^{\pi}[/tex] isn't the only answer for [tex](-1)^{1/i}[/tex], it depends on the branch of the logarithm you used. Can you find the other values? They might be even more suprising...
     
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