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Complex Numbers and Quadratic Equations: JEE Mains 2022 June 29 Shift 1

Hard· Argand plane and polar form· +4 / 0

Let

S=\{z\in\mathbb C:|z-2|\le1,\ z(1+i)+\bar z(1-i)\le2\}

. Let

|z-4i|

attains minimum and maximum values, respectively, at

z_1\in S

and

z_2\in S

. If

5\left(|z_1|^2+|z_2|^2\right)=\alpha+\beta\sqrt5

, where

\alpha

and

\beta

are integers, then the value of

\alpha+\beta

is equal to ______.

Your answer (numerical)

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