# i one u

Algebra Level 4

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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