Question 184
Prove for all complex numbers $z$ that
$$
|z|^2 + 2|z - 1| \ge 1,
$$
with equality iff $z = 1$.
$$
|z|^2 + 2|z - 1| \ge 1,
$$
with equality iff $z = 1$.
MathNet 2026 — Part 05 Question 184
Math Olympiad Vault · MathNet 2026 — Part 05
Math Olympiad Vault · MathNet 2026 — Part 05