Is This Complex Infinity Math Challenge Solvable?

[AlbertEinstein]

Math Teaser!

Can you solve this?

\frac{4 \infty}{\sqrt{-1}} {(1+\sqrt{-1})^(1/\infty)-(1-\sqrt{-1})^(1/\infty)} [\tex]<br /> <br /> Edit: why this latex is not being generated? Anyway the &quot;expression&quot; is<br /> <br /> [(4*inf)/sqrt(-1)] * { [1+sqrt(-1)]^(1/inf) - [1-sqrt(-1)]^(1/inf) }<br /> <br /> where inf stands for infinity.

 

[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.

 

[AlbertEinstein]

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

 

[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.

 

[quark]

I get zero as answer

 

[AlbertEinstein]

Nooooo..,O.K. I shall give a hint .Use polar forms of (1+i) and (1-i).
Give it a try.

 

[Jimmy Snyder]

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

 

[AlbertEinstein]

Yeah its correct.