Question 14
If $a$, $b$, $c$ are complex numbers of modulus $1$, prove that
$$
|a - b|^2 + |a - c|^2 - |b - c|^2 \ge -1.
$$
$$
|a - b|^2 + |a - c|^2 - |b - c|^2 \ge -1.
$$
MathNet 2010 — Part 05 Question 14
Math Olympiad Vault · MathNet 2010 — Part 05