Linear Quadratic Cubic Quartic

Algebra Level 3

\[ \begin{eqnarray} a \ \ + b \ + c \ \ &=& 2\\ a^{ 2 } + b^{ 2 } + c^{ 2 } &=& 6\\ a^{ 3 } + b^{ 3 } + c^{ 3 }&=& 8\\ \end{eqnarray} \] For complex numbers \(a,b,c\), we are given the system of equations above. Find the value of \( a^{ 4 } + b^{ 4 } + c^{ 4 } \).

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