The form z + 1/z

Algebra Level 2

If for zC ,z \in \mathbb{C} \space , z+1z=2cos6°.z+\dfrac{1}{z}=2 \cos 6°. Then find the value of (z1000+1z1000).\left( z^{1000}+\frac{1}{z^{1000}} \right).

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