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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Exponentation of Complex Numbers
Replies: 14   Last Post: Nov 13, 2008 3:36 PM

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Gerry Myerson

Posts: 4,919
Registered: 12/6/04
Re: Exponentation of Complex Numbers
Posted: Nov 10, 2008 1:14 AM
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In article <20081109202745.W14349@agora.rdrop.com>,
William Elliot <marsh@rdrop.remove.com> wrote:

> The rules of exponentation for reals are
>
> a^0 = 1
> (ab)^x = a^x b^x
> a^x a^y = a^(x + y)
> (a^x)^y = a^xy
>
> provided ab /= 0. In addition
>
> 0^x = 0
>
> provided x /= 0.
>
> Are all these rules valid for complex numbers?
> Is there a counter example to the forth rule?

The 2nd rule is problematical if, e.g.,
a = b = -1, x = 1/2.

--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)

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