i one u

Algebra Level 5

How many ordered triples of complex numbers \((x,y,z)\) satisfy the following system of equations:

\[\begin{array}{c c c c c c c c c } x &+& y &+& z &= &-1, \\ x^2 &+& y^2 &+& z^2 &= &-13&+32i, \\ x^3 &+& y^3 &+& z^3 &=& +95&-48i. \\ \end{array}\]

Details and assumptions

The imaginary unit is \(i\), which satisfies \(i^2=-1\).

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