Câu hỏi 53
Cho $n \in \mathbb{N}$, $n \ge 2$. Tìm tất cả $z \in \mathbb{C}$ sao cho:
$$
|z^{n+1} - z^n| \ge |z^{n+1} - 1| + |z^{n+1} - z|
$$
$$
|z^{n+1} - z^n| \ge |z^{n+1} - 1| + |z^{n+1} - z|
$$
Math Olympiad Vault · MathNet 2023-part-05 — 191 bài (EN–VI)