Question

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

A = {z : Im z ≥1}

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 :

A = set of points on and above the line y = 1 in the argand plane. B = set of points on the circle (x - 2)² + (y -1)² = 3²

C = set of point lies on the line x + y + = √2

Hence A∩B ∩C = has only one point of intersection.