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 \((x-y)(y-z)(z-x)?\)
by
Calvin Lin