Complexing

Algebra Level 3

The complex number \(z\) satisfies \( Im(z) > 0 \) and \(z+\dfrac 1z = \sqrt 3\). What positive integer \( n \leq 12 \) satisfies:

\[\large \frac {z^n + 1 }{z^n - 1 } = - i \cot \left(\frac{25π}{3}\right) \]

Notations:

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