JEE Main 2024 Mathematics question
The sum of the square of the modulus of the elements in the set {z = a + ib; a, b ∈ ℤ, z ∈ ℂ, |z − 1| ≤ 1, |z − 5| ≤ |z − 5i|} is ........
Answer: 9
Solution
|z − 1| ≤ 1 means (x − 1)² + y² ≤ 1, and |z − 5| ≤ |z − 5i| gives x ≥ y. The integer points satisfying both
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