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QJEEM22Mafc4b: JEE Main 2022 Mathematics - Class 11 JEEM22Mafc4b Solution: The number of elements in the set {z = a + ib C : a, b Z and 1…

The number of elements in the set {z = a + ib ∈\in C : a, b ∈\in Z and 1 < | z −- 3 + 2i | < 4} is __________.

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JEE Main 2022 (Online) 28th June Morning Shift Mathematics - Complex Numbers Question 80 English Explanation
at line y=−2y=-2 , we have (5,−2)(6,−2)(1,−2)(0,−2)(5,-2)(6,-2)(1,-2)(0,-2) ⇒4\Rightarrow 4 points

at line y=−1y=-1 , we have (4,−1)(5,−1)(6,−1)(2,−1)(4,-1)(5,-1)(6,-1)(2,-1) (1,−1)(0,−1)⇒6(1,-1)(0,-1) \Rightarrow 6 points

at line y=0y=0 , we have (0,0)(1,0)(2,0)(3,0)(4,0)(0,0)(1,0)(2,0)(3,0)(4,0) (5,0)(6,0)⇒7(5,0)(6,0) \Rightarrow 7 points

at line y=1y=1 , we have (1,1),(2,1),(3,1),(4,1),(5,1)(1,1),(2,1),(3,1),(4,1),(5,1) i.e. 5 points

symmetrically

at line y=−5y=-5 , we have 5 points

at line y=−4y=-4 , we have 7 points

at line y=−3y=-3 , we have 6 points

So Total integral points =2(5+7+6)+4=2(5+7+6)+4

=40=40

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