I need to find the zeros of $z^6-4z^5+z^2-1$ in the unit disk using Rouche's theorem.
The hint given is to consider the functions $g(z)=z^6-4z^5+z^2-1$ and $f(z)=-4z^5$. The issue is that the inequality $|f(z)-g(z)|<|f(z)$, that is, $|z^6+z^2-1|<4|z^5|$ does not seem to hold on the unit disk. What am I doing wrong?
Also, in general, how do you find the function $g$ required to apply Rouche's theorem?