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
example of said case by SilverKnight)
I know that ln(i)=(π/2)*i, but you need to prove it. I know it's true because it comes from the fact that e^(iπ)=-1, but then you'd need to prove that too. If you didn't need to prove it, then you could just say that e^(iπ)=-1 as your example...
Since it needs to be proven, I suppose I should ask you to, but then I'd get a long calculus proof I wouldn't understand... So I'm happy with your proof! Ah... such is the world of complex numbers!
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Posted by Tristan
on 2003-11-25 19:02:43 |
re: example of said case
