# 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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