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
solution by luminita)
Your solution is much better than mine because you avoid using the logarithm function. For your solution, we do have to believe e^(it)=cos(t)+i*sin(t) for real t and that the law of exponents (a^b)^c=a^(b*c) extends from the real numbers to the complex numbers (or, in other words, not very much). You have really scaled the problem down to essentials. Excellent!
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Posted by Richard
on 2003-11-26 19:00:29 |
re: solution
