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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 : -i; |z| = 1 and (z-1)/(z+1) is purely imaginary} contains infinitely many elements.

1. Both are correct
2. Only (S1) is correct
3. Only (S2) is correct
4. Both are incorrect

Correct answer: Only (S2) is correct

Solution

Statement (S2) is correct because the condition for (z-1)/(z+1) to be purely imaginary allows for an infinite number of points on the unit circle in the complex plane. In contrast, statement (S1) is incorrect as it describes a more restrictive condition that results in only two specific solutions.

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