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.
(In reply to
re: example of said case by Tristan)
Tristan, you've made a very good point.
It's always sort of a question about where does one stop 'proving' one's rules/postulates... and this one, I can understand, is somewhat confusing.
I don't think this is the appropriate forum for the proof of it, suffice it to say that it comes from the power series expansion of the irrational number, e, as well as the series expansion of both sin() and cos().
This link may be a good start if you would like to learn more about this subject.
Hope it helps.
-SK
re(2): example of said case
