Suppose $w$ is a complex number, and set $c=\max(1,|w|)$. If $F$ and $G$ are non-zero polynomials in one indeterminate with coefficients in $\mathbb{C}$, and $\deg(F)=d$ and \deg(G)=d', with $|F|,|G|\geq 1$. If $R$ is their resultant, then why is |R|\leq c^{d+d'}[|F(w)|+|G(w)|]|F|^{d'}|G|^d(d+d')^{d+d'}?
Here, I'm using $|F|$ to be the maximum of the absolute values of the coefficients of $F$. Thanks for any suggestions on approaching this.
The Source of this problem is Serge Lang's Algebra, exercise 16 of Chapter IV.