Among the statements (S1): The set {z ∈ C -{-i}:|z|=1. and (z-i)/(z+i) is purely real } contains exactly two elements, and (S2): The set {z ∈ C…

Among the statements (S1) : The set $\displaystyle \left\{z \in \mathbb{C}-\{-i\}:|z|=1\right.$ and $\displaystyle \frac{z-i}{z+i}$ is purely real $\displaystyle \}$ contains exactly two elements, and (S2) : The set $\displaystyle \left\{z \in \mathbb{C}-\{-1\}:|z|=1\right.$ and $\displaystyle \frac{z-1}{z+1}$ is purely imaginary $\displaystyle \}$ contains infinitely many elements.