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Complex Numbers question

2022 · 29 Jun · Shift 1 · Q36
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  5. /2022 · 29 Jun · Shift 1 · Q36

Complex Numbers question

2022 · 29 Jun · Shift 1 · Q36

JEE MainMathematicsComplex NumbersNumerical+4 / −1
Let S={z∈C:∣z−2∣≤1, z(1+i)+z‾(1−i)≤2}S = \{ z \in C:|z - 2| \le 1,\,z(1 + i) + \overline z (1 - i) \le 2\}S={z∈C:∣z−2∣≤1,z(1+i)+z(1−i)≤2}. Let ∣z−4i∣|z - 4i|∣z−4i∣ attains minimum and maximum values, respectively, at z1 ∈\in∈ S and z2 ∈\in∈ S. If 5(∣z1∣2+∣z2∣2)=α+β55(|{z_1}{|^2} + |{z_2}{|^2}) = \alpha + \beta \sqrt 55(∣z1​∣2+∣z2​∣2)=α+β5​, where α\alphaα and β\betaβ are integers, then the value of α\alphaα+β\betaβ is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
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