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JEE Main 1982 Mathematics question on Complex Numbers and Quadratic Equations

If z=(32+i2)5+(32−i2)5z = \left(\dfrac{\sqrt{3}}{2} + \dfrac{i}{2}\right)^5 + \left(\dfrac{\sqrt{3}}{2} - \dfrac{i}{2}\right)^5, then
  1. A.
    Re(z)=0(z) = 0
  2. B.
    Im(z)=0(z) = 0
  3. C.
    Re(z)>0(z) > 0, Im(z)>0(z) > 0
  4. D.
    Re(z)>0(z) > 0, Im(z)<0(z) < 0
Show answer

Correct option: B

[1982]

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