Among the statements (S1) : The set \(\left{\mathrm{z}\in \mathrm{ℂ}-{-\mathrm{i}}:|\mathrm{z}|=1\right.\) and \(\frac{\…

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

[JEE Main 2025, 7 Apr (Shift 1)]