Complex Power Operation: Is x^iy Possible?

  • Context: Undergrad 
  • Thread starter Thread starter scientificon
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Discussion Overview

The discussion revolves around the validity of complex power operations, specifically whether expressions like 2i^3 can be calculated or if they are considered undefined. The scope includes theoretical considerations of complex exponentiation.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant questions the validity of complex power operations, specifically asking if 2i^3 can be calculated or is undefined.
  • Another participant asserts that complex exponentiation is valid and references Euler's formula as support.
  • A third participant directs others to a FAQ post that discusses the topic further.
  • A fourth participant provides a definition of complex exponentiation, stating it is defined as x^y := e^(y log(x)).

Areas of Agreement / Disagreement

There appears to be no consensus on the initial question, as participants provide differing levels of support and references without resolving the validity of the specific operation in question.

scientificon
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I am wondering whether complex power operation is valid.

For example, can 2i3 be calculated? Or is it undefined?

Thanks
 
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See the FAQ post about this topic.
https://www.physicsforums.com/showthread.php?t=637214 .
 
Last edited by a moderator:
complex exponentiation is defined by

x^y:=e^(y log(x))
 

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