JEE Advance - Mathematics (1982 - No. 25)
If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5},$$ then
$${\mathop{\rm Re}\nolimits} \left( z \right) = 0$$
$${\rm I}m\left( z \right) = 0$$
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) > 0\,$$
$${\mathop{\rm Re}\nolimits} \left( z \right) > 0,\,{\rm I}m\left( z \right) < 0$$