Groups of Reciprocal Friends

Algebra Level 4

\[\left( x + \frac{1}{x} \right)^2 + \left( x^2 + \frac{1}{x^2} \right)^2 + \cdots + \left( x^{27} + \frac{1}{x^{27}} \right)^2\]

If \(x\) is a complex number satisfying \(x^2 + x + 1 = 0\), determine the value of the expression above.


Source: Trinity University
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