Let C be the set of all complex numbers. LetS1 = {z$\in$C : |z $-$ 2| $\le$ 1} and S2 = {z$\in$C : z(1 + i) + $\overline z $(1 $-$ i) $\ge$ 4}.Then, the maximum value of ${\left| {z - {5 \over 2}} \right|^2}$ for z$\in$S1 $\cap$ S2 is equal to :

Question

Let C be the set of all complex numbers. Let

S₁ = {z$\in$C : |z $-$ 2| $\le$ 1} and

S₂ = {z$\in$C : z(1 + i) + $\overline z $(1 $-$ i) $\ge$ 4}.

Then, the maximum value of ${\left| {z - {5 \over 2}} \right|^2}$ for z$\in$S₁ $\cap$ S₂ is equal to :

${{3 + 2\sqrt 2 } \over 4}$

${{5 + 2\sqrt 2 } \over 2}$

${{3 + 2\sqrt 2 } \over 2}$

${{5 + 2\sqrt 2 } \over 4}$

Solution

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