Point Operations in Square and Asymptotic Limits

OABC is a square where O is the origin and AB = 1. Consider the set of points $S = (x_i, y_i)$ in the square such that $x_i + y_i \le 1$. Let $P(x_1, y_1)$ and $Q(x_2, y_2)$ be two such points. Two operations addition (+) and multiplication (.) on S are defined as $P + Q = (x_1 + x_2 - x_1 x_2, y_1 y_2)$ $P . Q = (x_1 x_2, y_1 + y_2 - y_1 y_2)$

For a very large number n, $P^n + Q^n$ is

For a very large number n, $nP + nQ$ is