Roots and complex numbers

  • Thread starter cjellison
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  • #1
cjellison
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There are n nth roots to every complex number (except zero).

My question: How many "roots" are there when you take a complex number to an irrational or transcendental number. For that matter, how do we define raising a number to an irrational number? How do we define raising a number to a transcendental number?

Hmm...how is this defined? By a taylor series?

[tex]
e^{1/e}
[/tex]
 

Answers and Replies

  • #2
Hurkyl
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Science Advisor
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By definition, in the complexes:

[tex]z^w := \exp(w \mathop{\mathrm{Log}} z)[/tex]
 
  • #3
HallsofIvy
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In the complex plane, a number to an irrational (whether transcendental or not) power has an infinite number of values.
 

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