Question

If \( z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5 \), then

• A. \( \operatorname{Re}(z) > 0, \operatorname{Im}(z) < 0 \)
• B. \( \operatorname{Im}(z) = 0 \)
• C. \( \operatorname{Re}(z) = 0 \)
• D. \( \operatorname{Re}(z) > 0, \operatorname{Im}(z) > 0 \)

Hint:

When conjugate complex numbers are added after equal powers, their imaginary parts cancel and the result is real.

Answer 1

The Correct Option is B