Math Teaser

1. Oct 30, 2006

AlbertEinstein

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. Oct 30, 2006

Jimmy Snyder

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
3. Oct 30, 2006

AlbertEinstein

Sorry dude but I think its wrong.THe answer is something else.Btw it was a math teaser :)

4. Oct 30, 2006

daveb

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.

5. Nov 3, 2006

quark

I get zero as answer

6. Nov 3, 2006

AlbertEinstein

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
7. Nov 3, 2006

Jimmy Snyder

That's a lot of hint. Here's what I get now:
2 * pi
I hope I didn't screw up somewhere.

8. Nov 4, 2006

AlbertEinstein

Yeah its correct.

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