PYQ Vault
EbooksTutor

Area of a region bounded by a circle and lines in the complex plane

This type of question, asked 3 times: 4 Apr 2024, 5 Apr 2024, 22 Jan 2025. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    4 Apr 2024

    160
    The area (in sq. units) of the region S={z∈C;∣z−1∣≤2;(z+z‾)+i(z−z‾)≤2,lm(z)≥0}\mathbf{S = \{ z \in C;|z - 1| \leq 2;(z +}\overline{z}) + i(z -\overline{z}) \leq 2,lm(z) \geq 0\} is

    Tap an option to check your answer.

  2. Question 2

    5 Apr 2024

    153
    Let S1={z∈C:∣z∣≤5}S_{1}\mathbf{= \{ z \in C:|z| \leq 5\}}, S2={z∈C:Im(z+1−3i1−3i)≥0}S_{2}=\left\{ z \in C:Im\left( \frac{z + 1 -\sqrt{3}i}{1 -\sqrt{3}i} \right)\geq 0 \right\} and S3={z∈C:Re(z)≥0}S_{3}\mathbf{= \{ z \in C:Re(z) \geq 0\}}. Then the area of the region S1∩S2∩S3S_{1}\cap S_{2}\cap S_{3} is

    Tap an option to check your answer.

  3. Question 3

    22 Jan 2025

    144
    Let the curve z(1+i)+zˉ(1−i)=4,z∈Cz(1 + i) +\bar{z}(1 - i) = 4,z \in C, divide the region ∣z−3∣≤1|z - 3| \leq 1 into two parts of areas α\alpha and β\beta. Then ∣α−β∣|\alpha - \beta| equals :

    Tap an option to check your answer.