Let C be the set of all complex numbers. Let S₁ = z C: |z - 2| ≤ 1 and S₂ = z C: z(1 + i) + z (1 - i) ≥ 4. Then, the maximum value of | z - 5/2 |² for z S₁ S₂ is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Jul, Evening shift · Q3189

JEE Main 202127 Jul, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let C be the set of all complex numbers. Let S₁ = {z

\in

C : |z

-

\le

1} and S₂ = {z

\in

C : z(1 + i) +

\overline z

-

\ge

4}. Then, the maximum value of

{\left| {z - {5 \over 2}} \right|^2}

for z

\in

S₁

\cap

S₂ is equal to :