Question 141
Given complex numbers $a$, $b$, $c$, let $|a+b| = m$, $|a-b| = n$, and suppose $mn \neq 0$. Prove that
$$
\max\{|ac + b|, |a + bc|\} \ge \frac{mn}{\sqrt{m^2 + n^2}}
$$
$$
\max\{|ac + b|, |a + bc|\} \ge \frac{mn}{\sqrt{m^2 + n^2}}
$$
MathNet 2007-part-01 — 187 problems (EN–VI) Question 141
Math Olympiad Vault · MathNet 2007-part-01 — 187 problems (EN–VI)