An algebra problem by Dev Sharma

Algebra Level 5

\[ \large{\begin{cases} x&+&y&+&z&=& 0 \\ x^3 &+& y^3 &+& z^3& =& 18 \\ x^7 &+& y^7 &+ &z^7 &=& 2058 \end{cases}} \]

If \(x,y\) and \(z\) are complex numbers that satisfy the system of equations above and \(x^2 + y^2 + z^2 > 0 \), find the value of \(x^{10} + y^{10} + z^{10} \).

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