# 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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