QJEEM24Ma19b8: JEE Main 2024 Mathematics - Class 11 JEEM24Ma19b8 Solution: The area (in sq. units) of the region S = { z ∈ C :

Question

Verified Solution • 2025–26 Session moderate

The area (in sq. units) of the region $S = {z \in C : | z - 1 | \leq 2; (z + \bar{z}) + i (z - \bar{z}) \leq 2, lm (z) \geq 0}$ is

Accepted Answer

$| z - 1 | \leq 2 \Rightarrow (x - 1)^{2} + y^{2} = 4$

$\begin{aligned} z + \bar{z} + i (z - \bar{z}) \leq 2 \\ \Rightarrow & x - y \leq 1 \\ Im (z) \geq 0 \\ \Rightarrow & y \geq 0 \end{aligned}$

JEE Main 2024 (Online) 4th April Evening Shift Mathematics - Complex Numbers Question 17 English Explanation

$\begin{aligned} Required area = (\frac{\frac{3 π}{4}}{2 π}) (π) (2)^{2} \\ = \frac{3}{2} π \end{aligned}$

Step-by-Step Verified Solution