Is the Complex Number Identity True for Imaginary Numbers and Integer Powers?

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Discussion Overview

The discussion revolves around the validity of the complex number identity involving imaginary numbers and integer powers, specifically examining the expression n^{ \frac{2i\pi n}{log}} and its implications. The scope includes conceptual understanding of complex numbers and logarithmic notation.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant proposes that n^{ \frac{2i\pi n}{log}} equals 1 for integer n, expressing belief in the identity's truth.
  • A second participant, also new to the forum, seeks clarification on the term (2ipin)/log, indicating potential unfamiliarity with the notation used.
  • Another participant asserts that "log" by itself is meaningless without a specified argument, suggesting a need for clarity in the expression.
  • A participant expresses an intention to prove the identity but encounters difficulty due to the vague reference to "log of thin air."
  • A link to a Wikipedia article on roots of unity is provided as a resource for further insight into the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the identity, and there are multiple competing views regarding the interpretation of the logarithmic term.

Contextual Notes

The discussion highlights limitations in the clarity of notation and definitions, particularly concerning the use of "log" without an argument, which may affect understanding of the identity being discussed.

Who May Find This Useful

Readers interested in complex numbers, logarithmic functions, and mathematical identities may find this discussion relevant.

zetafunction
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let be n and integer and 'i' the imaginary unit

is then true that [tex]n^{ \frac{2i\pi n}{log}} =1[/tex]

i believe that is true
 
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zetafunction said:
let be n and integer and 'i' the imaginary unit

is then true that [tex]n^{ \frac{2i\pi n}{log}} =1[/tex]

i believe that is true
new to this forum
and newish to complex numbers
could you explain what (2ipin)/log is?
ie what is something/log
It may be that I am unfamiliar with the notation
thanks
 
log by itself is meaningless. You need log(something).
 
thanks
I thought I would try and prove the identity but then got stuck on log of thin air
 

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