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