Find the complex solutions

Algebra Level 4

\[\large \begin{cases} {x^5 + y^5=33} \\ {x+y=3 } \end{cases} \]

If the system of equations above has two real and two complex solutions, what is the value of \(x^2+y^2\) when \(x,y\) are both not real numbers?

Note that \(a + b\sqrt{-1} \) is a complex number where \(a,b\) are real numbers.

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