I have to find out how many roots the polynomial
has in the first quadrant.
Certainly, I need to use the argument principle, but I don't see how. Here's what I tried.
All zeroes of lie in which follows from applying the Cauchy bound. Suppose I can prove that has no real and no imaginary roots. Then, since the function is holomorphic, I have to calculate
(integrals have to be calculated in the appropriate directions of course).
But to calculate those integrals, don't I need to know the zeroes of Only then would I be able to integrate by residues, right? It's supposed to be very simple.