JEE Mains · Maths · STD 11 - 4.1 complex nubers
Among the statements
(S1) : The set \(\left\{\mathrm{z} \in \mathbb{C}-\{-\mathrm{i}\}:|\mathrm{z}|=1\right.\) and \(\frac{\mathrm{z}-\mathrm{i}}{\mathrm{z}+\mathrm{i}}\) is purely real} contains exactly two elements, and (S2) : The set \(\left\{\mathrm{z} \in \mathbb{C}-\{-1\}:|\mathrm{z}|=1\right.\) and \(\frac{\mathrm{z}-1}{\mathrm{z}+1}\) is purely imaginary contains infinitely many elements.
- A both are incorrect
- B only (S1) is correct
- C only (S2) is correct
- D both are correct
Answer & Solution
Correct Answer
(C) only (S2) is correct
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{S}_1:|\mathrm{z}|=1, \frac{\mathrm{z}-\mathrm{i}}{\mathrm{z}+\mathrm{i}}=\frac{\overline{\mathrm{z}}+\mathrm{i}}{\overline{\mathrm{z}}-\mathrm{i}} \\ &…
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