JEE Mains · Maths · STD 11 - 4.1 complex nubers
The sum of the square of the modulus of the elements in the set \(\{z=a+i b: a, b \in Z, z \in C,|z-1| \leq 1,|z-5| \leq|z-5 i|\}\) is ........
- A \(10\)
- B \(9\)
- C \(5\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
\( |z-1| \leq 1 \) \( \Rightarrow|(x-1)+i y| \leq 1 \) \( \Rightarrow \sqrt{(x-1)^2+y^2} \leq 1 \) \( \Rightarrow(x-1)^2+y^2 \leq 1 ............(1)\) Also \(|z-5| \leq|z-5 i|\) \( (x-5)^2+y^2 \leq x^2+(y-5)^2 \) \( -10 x \leq-10 y \) \( \Rightarrow x \geq y.........(2)\) Solving…
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