# Complexing

Algebra Level 4

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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