A complex system

Algebra Level 5

Suppose that x,x, y,y, and zz are distinct complex numbers, such that

{x+y+z=1x2+y=y2+z=z2+x. \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)?(x-y)(y-z)(z-x)?

Calvin Lin by Calvin Lin
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