Complex Numbers

Geometry Level 5

Complex numbers \(a\), \(b\) and \(c\) are the zeros of a polynomial \(P(z) = z^3+qz+r\), and \(|a|^2+|b|^2+|c|^2=250\). The points corresponding to \(a\), \(b\), and \(c\) in the complex plane are the vertices of a right triangle with hypotenuse \(h\). Find \(h^2\).

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