Is it possible for two complex numbers to have a real exponentiation?

In other words, if x and y are complex (each have the form a+bi), show that x^y can have a real value, or prove that it is impossible.

Note: i is the imaginary value defined as the number that yields -1 when squared. a and b are any real numbers, but b is not 0.

log=(log to base e).
log(x^y)=ylogx.
x^y=e^(ylogx).
Let y=i, x=e^(it) with t real and not a multiple of pi so that x is not real. Then
x^y=e^(i(it))=e^(-t)=real.
Edited on November 25, 2003, 10:05 pm

Posted by Richard on 2003-11-25 18:53:12