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Question 62

Let $$z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5$$. If $$R(z)$$ and $$I(z)$$ respectively denote the real and imaginary parts of $$z$$, then:

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