A Cyclic Complex Maximum

★ 9/10complex numbers AM-GM inequality Symmetry

Problem

Complex numbers $a, b, c$ satisfy $|a|^2 + |b|^2 + |c|^2 = 1$ . Find the maximum value of

f = \left|ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2)\right|.

Answer

Solution

Difficulty	9/10
Topics	complex numbers, AM-GM, inequality, Symmetry

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