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Complex System Minimize Product Squared

2175ExpertComplex NumbersSystems Of EquationsAlgebra

AIME II · 2012 · Problem 8

The complex numbers $z$ and $w$ satisfy the system $$ z + \frac{20i}w = 5+i$$ $$w+\frac{12i}z = -4+10i $$ Find the smallest possible value of $\vert zw\vert^2$.
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