Complex Number Statements (Jee Mains)

Geometry and Locus of Complex Numbers

Medium

Complex Number Statements

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

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