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