Let {\P}=\{ {\z} \in C:| {\z}+2-3 {\i}| \leq 1\} and {\Q}=\{ {\z} \in C: {\z}(1+ {\i})+\overline{ {\z}}(1- {\i}) \leq-8\}. Let in {\P} \cap {\Q},| {\z}-3+2 {\i}| be maximum and minimum at z_1 and z_2 respectively. If {|z_1 |}^2+2 z|^2=\alpha+\beta \sqrt{2}, where \alpha, \beta are integers, then \alpha+\beta equals______ [1-Feb-2024 Shift 1]

JEE Main 1-Feb-2024 Shift 1 Solved Paper

Section: Mathematics

Question : 27 of 90

Marks: +1, -0

Let P={z∈C:|z+2−3i|≤1} and Q={z∈C:z(1+i)+z(1−i)≤−8}. Let in P∩Q,|z−3+2i| be maximum and minimum at z1 and z2 respectively. If |z1|2+2z|2=α+β√2, where α,β are integers, then α+β equals______

[1-Feb-2024 Shift 1]

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