Let be any complex number such that is a purely imaginary number. Then is :

Let (z-i)/(z+i) = ik with k real. Solving gives |z|=1. Then z+1/z = z + ̅z = 2Re(z). Since |z|=1, Re(z) ∈ [-1,1], so z+1/z ∈ [-2,2]. For k=0, z=i gives 0, but if 0 is considered purely imaginary, z=i is allowed; if not, 0 is excluded. The value 1 occurs for z=e^{iπ/3}. Among options, B is the only one describing a real set (non-zero real numbers except 1), though the actual set is all reals in [-2,2] except 0 (or including 0). Given the options, B is the most appropriate.