Recent content by arithmuggle

Ahh thank you so much. I see that version of the theorem in Ahlfors. Although, I don't see why I would ever use the version of the theorem I had originally quoted since clearly having that extra "$ + \left| g(z) \right|$ " makes these inequalities a heck of a lot easier.

Question: Find the number of zeroes of the equation $ z^7 - 2z^5 + 6z^3 - z+1 = 0 $, in the unit disk. We have Rouche's theorem which says that if f(z) and g(z) are two functions analytic in a neighborhood of the closed unit disk and if |f(z) - g(z)| < |f(z)| for all z on the boundary of...