JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(\mathrm{C}\) be the set of all complex numbers. Let \(\mathrm{S}_{1} =\left\{\mathrm{z} \in \mathrm{C}|| \mathrm{z}-3-\left.2 \mathrm{i}\right|^{2}=8\right\}\) \(\mathrm{S}_{2} =\{\mathrm{z} \in \mathrm{C} \mid \operatorname{Re}(\mathrm{z}) \geq 5\} \text { and }\) \(\mathrm{S}_{3} =\{\mathrm{z} \in \mathrm{C} \| \mathrm{z}-\bar{z} \mid \geq 8\}\) Then the number of elements in \(\mathrm{S}_{1} \cap \mathrm{S}_{2} \cap \mathrm{S}_{3}\) is equal to:
- A \(1\)
- B \(0\)
- C \(Infinite\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
\(\mathrm{S}_{1}:|\mathrm{x}-3-2 i|^{2}=8\) \(|\mathrm{x}-3-2 \mathrm{i}|=2 \sqrt{2}\) \((\mathrm{x}-3)^{2}+(\mathrm{y}-2)^{2}=(2 \sqrt{2})^{2}\) \(\mathrm{~S}_{2}: \mathrm{x} \geq 5\) \(\mathrm{~S}_{3}:|\mathrm{z}-\overline{\mathrm{z}}| \geq 8\) \(|2 \mathrm{i} y| \geq 8\)…
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