# An algebra problem by حسن العطية

Algebra Level 3

Let $$x$$ and $$y$$ be real numbers satisfying $$x^2+y^2=11$$ and $$x^2-9 = y^2-16$$. Given that $$z = \sqrt{x^2+16} + i \sqrt{y^2+ 9}$$. Write $$z$$ as its polar coordinates.

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