I'm now solving the following complex analysis problem.
"determine the form of rational function in a plane hat has a positive value on unit circle."
hint suggested me that such a rational function must have same number of zeros and poles inside unit disk. But I cannot understand that. Using symmetry(Schwarz reflection principle) I can see that number of poles(zeros) inside unit disk is equal to number of poles(zeros) outside unit disk. BUT I CANNOT SEE WHY NUMBER OF POLES AND ZEROS MUST BE EQUAL..
can anybody give me some suggestion?