# A Fifth Root

Algebra Level 3

Suppose $$z$$ is a complex number such that $$z^5 = -\sqrt{3} + i$$ and $$z = \sqrt[5]{2} ( \cos n^{\circ} + i \sin n^{\circ})$$, where $$270 < n < 360$$. Find the exact value of $$n$$.

Details and assumptions

$$i$$ is the imaginary unit, where $$i^2=-1$$.

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