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