Complex Numbers 2 Question 29
30. The number of elements in the set $A \cap B \cap C$ is
(a) 0
(b) 1
(c) 2
(d) $\infty$
Match the Columns
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Answer:
Correct Answer: 30. True
Solution:
- Let $z=x+i y$
Set $A$ corresponds to the region $y \geq 1$
Set $B$ consists of points lying on the circle, centre at $(2,1)$ and radius 3.
i.e.
$$ x^{2}+y^{2}-4 x-2 y=4 $$
Set $C$ consists of points lying on the $x+y=\sqrt{2}$
Clearly, there is only one point of intersection of the line $x+y=\sqrt{2}$ and circle $x^{2}+y^{2}-4 x-2 y=4$.
