The answer is \(n^2\)

Algebra Level 4

\[\large \frac{31}{2- \alpha_1}+ \frac{31}{2- \alpha_2}+\frac{31}{2- \alpha_3} +\frac{31}{2- \alpha_4}\]

Given that \(1,\alpha_1, \alpha_2, \alpha_3,\alpha_4\) are distinct fifth roots of unity, evaluate the expression above.

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