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.

yes, it is possible:
i^i=e^(-pi/2)

Proof:
if a=0 and b=1, the complex number is z=i
i = cos(pi/2) + i in(pi/2)= e^(i(pi/2))
i^i = e^(i(pi/2))^i= e^(-pi/2) which is a real number

Posted by luminita on 2003-11-26 15:09:01