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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