Is it possible to calculate something like ?

I recall reading somewhere that is calculable (I think its a real number), so I was pondering whether or not this was true for complex numbers in general?

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- March 25th 2011, 09:14 PMjamixraising complex numbers to complex exponents?
Is it possible to calculate something like ?

I recall reading somewhere that is calculable (I think its a real number), so I was pondering whether or not this was true for complex numbers in general? - March 25th 2011, 09:20 PMdwsmith
- March 25th 2011, 09:25 PMdwsmith
- March 25th 2011, 09:29 PMjamix
Ah I think I just figured it out...

First you put the bottom number into polar coordinates . Then you break up the exponent so we have the following:

= = - March 25th 2011, 09:42 PMProve It
Yes you can. It's no simple task, but it requries you write the complex number in its exponential-polar form.

Complex Exponentiation -- from Wolfram MathWorld - March 25th 2011, 10:05 PMjamix
The Wolfram link really helped me understand what was being said in the other thread (which I couldn't follow).

- March 25th 2011, 10:06 PMdwsmith
- March 25th 2011, 10:23 PMProve It
- March 25th 2011, 10:24 PMdwsmith
- March 25th 2011, 10:30 PMdwsmith
Natural Logarithm -- from Wolfram MathWorld

Middle way down. - March 25th 2011, 11:02 PMCaptainBlack