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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 $z$ ?