Question

Let $C$ denote the set of all complex numbers and let us define two sets A and B as $A=\{z:z\in C$ and $\arg (z-i)\ge \frac{\pi }{3}\}$, where arg represents principal arguments and $B=\{z:z\in C$ and $|z-i|\le 1\}$. Then which of the following is (are) correct statement?

• A. $A\cap B$ represents complex numbers lying inside or on boundary of segment of a circle.
• B. set $B$ is subset of set A.
• C. $A\cap B$ represents complex numbers lying on an arc of a circle.
• D. $A\cap B$ represents complex numbers lying inside of boundary of segment of a circle.

Answer 1

Answer: (A), (C), (D)

Correct answer is (a) $A\cap B$ represents complex numbers lying inside or on boundary of segment of a circle. Correct answer is (c) $A\cap B$ represents complex numbers lying on an arc of a circle. Correct answer is (d) $A\cap B$ represents complex numbers lying inside of boundary of segment of a circle.