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 \-1: |z| = 1 and (z - 1)/(z + 1) is purely imaginary contains infinitely many elements. Which of the following is correct?

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q186

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Among the statements: (S1): The set

\{ z \in \mathbb{C} \setminus \{-i\} : |z| = 1 \text{ and } \frac{z - i}{z + i} \text{ is purely real} \}

contains exactly two elements, and (S2): The set

\{ z \in \mathbb{C} \setminus \{-1\} : |z| = 1 \text{ and } \frac{z - 1}{z + 1} \text{ is purely imaginary} \}

contains infinitely many elements. Which of the following is correct?

JEE Main 2025 · April, Unspecified (session-level dataset) · Q186

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Among the statements: (S1): The set

\{ z \in \mathbb{C} \setminus \{-i\} : |z| = 1 \text{ and } \frac{z - i}{z + i} \text{ is purely real} \}

contains exactly two elements, and (S2): The set

\{ z \in \mathbb{C} \setminus \{-1\} : |z| = 1 \text{ and } \frac{z - 1}{z + 1} \text{ is purely imaginary} \}

contains infinitely many elements. Which of the following is correct?