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(2): example of said case by SilverKnight)
I think that the problem itself is assuming that the solver knows what x^y means for complex x and y. Anybody who knows that must also know that i=e^(i*pi/2) and that log() and e^() are inverses. A good reference text is Marsden and Hoffman, "Basic Complex Analysis", 2nd Ed., pp 27-44, for those who want to study up. This is not pre-university material, except perhaps for the gifted.
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Posted by Richard
on 2003-11-25 22:56:42 |
re(3): example of said case
