The number of elements in the set A∩B∩C is (A) 0 (B) 1 (C) 2

Question

Read the following passage and answer the questions. 

Let A, B, C be three sets of complex number as defined below

A = {z: |I_m z ≥ |} 

B = {z: |z – 2 – i| = 3} 

C = {z: Re ((1 – i)z) + √2) 

The number of elements in the set A∩B∩C is 

(A) 0 

(B) 1 

(C) 2 

(D) ∞

Answer 1

Correct option (B) 1
Explanation:

Let z = x + iy

Set A corresponds to the region 

y ≥ 1… (i)

Set B consists of points lying on the circle,, centre at (2, 1) and radius 3

i.e.x² + y² – 4x – 2y = 4 ….(ii) 

Set C consists of point lying on the

x + y = √2  … (iii)