A complex system

Algebra Level 5

Suppose that \(x,\) \(y,\) and \(z\) are distinct complex numbers, such that

\[ \begin{cases} x+y+z=1 \\ x^2+y=y^2+z=z^2+x.\\ \end{cases} \]

What is the value of \((x-y)(y-z)(z-x)?\)

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