JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(S _{1}, S _{2}\) and \(S _{3}\) be three sets defined as \(S _{1}=\{ z \in C :| z -1| \leq \sqrt{2}\}\) ; \(S _{2}=\{ z \in C : \operatorname{Re}((1- i ) z ) \geq 1\}\) ; \(S _{3}=\{ z \in C : \operatorname{Im}( z ) \leq 1\}\) Then the set \(S _{1} \cap S _{2} \cap S _{3}\)
- A is a singleton
- B has exactly two elements
- C has infinitely many elements
- D has exactly three elements
Answer & Solution
Correct Answer
(C) has infinitely many elements
Step-by-step Solution
Detailed explanation
For \(|z-1| \leq \sqrt{2}, z\) lies on and inside the circle of radius \(\sqrt{2}\) units and centre \((1,0) .\) For \(S _{2}\) Let \(z=x+i y\) Now, \((1-i)(z)=(1-i)(x+\) iy \()\) \(\operatorname{Re}((1-i) z)=x+y\) \(\Rightarrow x+y \geq 1\)…
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