A Fifth Root

Algebra Level 3

Suppose z z is a complex number such that z5=3+i z^5 = -\sqrt{3} + i and z=25(cosn+isinn) z = \sqrt[5]{2} ( \cos n^{\circ} + i \sin n^{\circ}) , where 270<n<360 270 < n < 360 . Find the exact value of n n .

Details and assumptions

ii is the imaginary unit, where i2=1i^2=-1.

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