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

The inequality |z-4| < |z-2| represents the region given by

The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1$$ lie on

The smallest positive integer n for which $${\left( {{{1 + i} \over {1 - i}}} \right)^n} = 1$$ is