Let S₁={z∈C:|z−2|≤1} and S₂=... | Complex Numbers

JEE MAIN 2021 S2

27-07-2021 S2

Question

Let be the set of all complex numbers. Let $$ \begin{aligned} & S_1=\{z \in \mathbb{C}:|z-2| \leq 1\} \text { and } \\ & S_2=\{z \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \geq 4\} \end{aligned} $$ Then, the maximum value of $\left|\mathbf{z -} \frac{\mathbf{5}}{\mathbf{2}}\right|^2$ for $\mathbf{z} \in \mathrm{S}_1 \cap \mathrm{~S}_2$ is equal to:

Select the correct option:

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

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

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

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution