let $f(z)=(z^2+9)(z^2+1)(z^2-1)+z^5(z^2+4)$. How many zeroes does $f$ has in $\{z|\operatorname{Re}{z}<0\}$.
I want to use the argument principle, but the integral is too long. I think I need to work with winding numbers, but I don't know how. Edit 1: I know form my teacher that there should be 6 zeroes.