Class 11Mathematics1 Complex Numbers and Quadratic Equations: Complex NumbersDe Moivre's theorem and Roots of unity
DifficultLet $z = \left( \frac{\sqrt{3}}{2} + \frac{i}{2} \right)^5 + \left( \frac{\sqrt{3}}{2} - \frac{i}{2} \right)^5$. If $R(z)$ and $I(z)$ respectively denote the real and imaginary parts of $z$,then:
- A$R(z) = -3$
- B$R(z) > 0$ and $I(z) > 0$
- C$R(z) < 0$ and $I(z) > 0$
- D$I(z) = 0$
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