I'm asked questions like to find the zeros, and multplicities of the $\mathbb{C}$-polynomials
$f(z) =z^6 +4z^2 - 1 \hspace{10mm} , |z| < 1$ or worse yet $f(z)=z^{87}+36z^{57}+71z^4+z^3-z+1 \hspace{10mm}, 1<|z|<2$
Surely factoring these things isn't the right approach...and I can't seem to think of a way to find them otherwise? We've been looking at some nice things we can do if we know what the zeros/singularities are, but as for finding them.. I don't know.
Thanks for any push in the right direction!