Mock AIME 3 Pre 2005 Problems/Problem 4

Problem

and are complex numbers such that

$\begin{align*}\zeta_1+\zeta_2+\zeta_3&=1\\ \zeta_1^2+\zeta_2^2+\zeta_3^2&=3\\ \zeta_1^3+\zeta_2^3+\zeta_3^3&=7\end{align*}$ (Error compiling LaTeX. Unknown error_msg)

Compute .

Solution

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