Question 53
Let $n \in \mathbb{N}$, $n \ge 2$. Determine all $z \in \mathbb{C}$ such that:
$$
|z^{n+1} - z^n| \ge |z^{n+1} - 1| + |z^{n+1} - z|
$$
$$
|z^{n+1} - z^n| \ge |z^{n+1} - 1| + |z^{n+1} - z|
$$
MathNet 2023-part-05 — 191 problems (EN–VI) Question 53
Math Olympiad Vault · MathNet 2023-part-05 — 191 problems (EN–VI)