Complex Rectangle

Algebra Level 3

Let \(z=x+iy\) be a complex number where \(x\) and \(y\) are integers. Find the area of the rectangle whose vertices are the roots of the equation \[\large z \bar{z}^3+\bar{z}z^3=350.\]

Details: \( \bar{z}=x-iy\) and \(i=\sqrt{-1}\).

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