Is This Complex Infinity Math Challenge Solvable?

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Discussion Overview

The discussion revolves around a mathematical challenge involving complex infinity, specifically an expression that includes limits and complex numbers. Participants explore various approaches to solving the problem, which appears to be framed as a teaser rather than a straightforward question.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents a mathematical expression involving infinity and complex numbers, seeking a solution.
  • Another participant proposes a limit approach, suggesting that the expression evaluates to 8, though they express uncertainty about the classification of the problem.
  • A different participant contests this answer, implying that the solution is incorrect and suggesting that the teaser nature of the problem should be acknowledged.
  • One participant hints that the expression can be related to hyperbolic sine and mentions the use of L'Hospital's rule to resolve indeterminacy.
  • Another participant claims to arrive at a solution of zero, indicating a different interpretation of the problem.
  • A subsequent reply suggests using polar forms of the complex numbers involved, indicating a potential method for simplification.
  • Finally, one participant arrives at a solution of 2 * pi, expressing hope that their calculation is correct, while another participant confirms this result.

Areas of Agreement / Disagreement

Participants express differing views on the correct solution to the mathematical challenge, with multiple competing answers presented. There is no consensus on a single correct answer, and the discussion remains unresolved regarding the final solution.

Contextual Notes

The discussion includes various assumptions about the behavior of limits involving complex numbers and the application of mathematical techniques like L'Hospital's rule. Some steps in the reasoning are not fully resolved, and participants rely on different interpretations of the original expression.

Who May Find This Useful

Individuals interested in complex analysis, limit evaluation, and mathematical problem-solving may find this discussion relevant.

AlbertEinstein
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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.
 
Last edited:
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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:
Sorry dude but I think its wrong.THe answer is something else.Btw it was a math teaser :)
 
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.
 
I get zero as answer
 
Nooooo..,O.K. I shall give a hint .Use polar forms of (1+i) and (1-i).
Give it a try.
 
Last edited:
That's a lot of hint. Here's what I get now:
2 * pi
I hope I didn't screw up somewhere.
 
Yeah its correct.
 

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