Condition for $z$ to $|P(z)|\lt 1$

Question

I want to investigate when it's true that $\sum_{n = 0}^{\infty}{(P(z))^n} = \frac{1}{1-P(z)}$ where $P(z)$ is a complex polynomial. I think the condition is $|P(z)|\lt 1$ but I don't know how to get condition for $z$ from this. Maybe triangle inequality is useful here.