Three Complex Products

★ 5/10complex numbers Substitution algebra

Problem

Complex numbers $x, y, z$ satisfy

\begin{cases} xy = -80 - 320\mathrm{i}, \\ yz = 60, \\ zx = -96 + 24\mathrm{i}. \end{cases}

Find $|x + y + z|^2$ .

Answer

Solution

Difficulty	5/10
Topics	complex numbers, Substitution, algebra

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