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Algebra Level 2

In the following equations \(x\) and \(y\) are complex numbers.

\(\begin{cases} \sqrt [ 4 ]{ \frac { { x }^{ 2 } }{ y } } =1 \\ { x }^{ 2 }+{ y }^{ 2 }=0 \\ xy=z \end{cases}\)

Find the product of all possible values of \(z\)?

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