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Algebra Level 5

112n=124(zn+1zn)2 \displaystyle \dfrac{1}{12} \sum_{n=1}^{24} \left ( z^{n} + \dfrac{1}{z^{n}} \right )^{2}

What is the value of the expression above if we are given that z2z+1=0z^{2} - z + 1 = 0 ?

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