>>23
The powers of real and imaginary numbers are generally defined in terms of the exponential function.
things like 2^3 have obvious meanings, but a^b for arbitrary a and b in the reals the meanings not so clear.
So using the exponential function which is quite easy to define in terms of real numbers, and it's inverse the logarithm we say that.
a^b = exp(b*log(a))
which has a definite expression in terms of real power series that we know converge (Given certain restrictions on a)
This can then be extended quite easily for complex a and b, given that we first extend our definitions of the complex exponential and logarithmic functions.
Make sense?