I'm performing a Von Neumann stability analysis for a finite difference scheme, and I need to derive a condition on my coefficients $B,C$ such that the moduli of the roots of the polynomial
$$P(z)=(1+B(1-e^{i\theta}))z^{n+1}-z^n-Ce^{-i\theta}$$
are bounded above by 1 for all $n\in\mathbb{N}, \ \theta\in[0,2\pi]$. One technique I've seen involves Rouche's theorem, but I'm unsure how to go about this. I've read elsewhere that the trick is to split up the polynomial into two parts, and determine the location of the zeros based on the dominating part, but I'm unsure how to apply this in this situation, since I'm looking to derive a condition that would ensure the roots of $P(z)$ are in the unit disk, instead of proving that the roots are in the unit disk for fixed $B,C$. How might I go about deriving a condition on $B$ and $C$ to ensure the roots of $P(z)$ are $\leq 1$?