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Paragraph: Let A, B, C be three sets of complex numbers as defined below. A= z ; lm z 1 ; B= z:|z-2-i|=3 ; C= z: Re ((1-i) z)= 2 . Question: The number of elements in the set A B C is

Options

  1. A0
  2. B1
  3. C2

Correct answer

B. 1

Step-by-step solution

Let z=x+i y Set A corresponds to the region y 1 . Set B consists of points lying on the circle, centred 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= 2 Clearly, there is only one point of intersection of the line x+y= 2 and circle x^2+y^2-4 x-2 y=4 .

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