Complex Rectangle

Algebra Level 3

Let z=x+iyz=x+iy be a complex number where xx and yy are integers. Find the area of the rectangle whose vertices are the roots of the equation zzˉ3+zˉz3=350.\large z \bar{z}^3+\bar{z}z^3=350.

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

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