1. The problem statement, all variables and given/known data A function f is analytic in the whole complex plane beside 4 poles. We know that -1,2,1+5i are poles of f and that f gets only real values in (-1,2). Find the fourth pole of f and show that f is a real-valued function for every real z which isn't a pole. 2. Relevant equations 3. The attempt at a solution I've tried using the symmetry principle but without any success.. Help is needed Thanks !