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Math Teaser

  1. Oct 30, 2006 #1
    Math Teaser!!

    Can you solve this?

    [tex] \frac{4 \infty}{\sqrt{-1}} {(1+\sqrt{-1})^(1/\infty)-(1-\sqrt{-1})^(1/\infty)} [\tex]

    Edit: why this latex is not being generated? Anyway the "expression" is

    [(4*inf)/sqrt(-1)] * { [1+sqrt(-1)]^(1/inf) - [1-sqrt(-1)]^(1/inf) }

    where inf stands for infinity.
     
    Last edited: Oct 30, 2006
  2. jcsd
  3. Oct 30, 2006 #2
    Answer:
    Taking the limit as N approaches infinity of

    4N/i * [ (1+i)^(1/N) - (1-i)^(1/N) ]

    which is:

    4N/i * [ 1 + i(1/N) + o(N^-2) - 1 + i(1/N) + o(N^-2) ]

    = 4N/i * [ 2i/N] + o(N^-1)

    I get 8.

    I'm not sure this is a brain teaser though.
     
    Last edited: Oct 30, 2006
  4. Oct 30, 2006 #3
    Sorry dude but I think its wrong.THe answer is something else.Btw it was a math teaser :)
     
  5. Oct 30, 2006 #4
    Hint: The part in the parenthesis is a hyperbolic sine, and the result is indeterminate until you apply L'Hospital's to get the final answer.
     
  6. Nov 3, 2006 #5
    I get zero as answer
     
  7. Nov 3, 2006 #6
    Nooooo..,O.K. I shall give a hint .Use polar forms of (1+i) and (1-i).
    Give it a try.
     
    Last edited: Nov 4, 2006
  8. Nov 3, 2006 #7
    That's a lot of hint. Here's what I get now:
    2 * pi
    I hope I didn't screw up somewhere.
     
  9. Nov 4, 2006 #8
    Yeah its correct.
     
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