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JEE Main202127 Jul 2021Morning ShiftMathematicsComplex NumberActual

Let C be the set of all complex numbers. Let S 1 = z ∈ C | z – 3 – 2 i 2 = 8 , S 2 = z ∈ C | Re z ≥ 5 and S 3 = z ∈ C | z – z ¯ ≥ 8 . Then the number of elements in S 1 ∩ S 2 ∩ S 3 is equal to

Options

  1. A1
  2. B0
  3. C2
  4. DInfinite

Correct answer

A. 1

Step-by-step solution

S 1 : z - 3 - 2 i 2 = 8 ⇒ z - 3 - 2 i = 2 2 ⇒ x - 3 2 + y - 2 2 = 2 2 2 (Put z = x + i y ) S 2 : x ≥ 5 S 3 : z - z ¯ ≥ 8 (put z = x + i y ) ⇒ 2 i y ≥ 8 ⇒ 2 y ≥ 8    ∴   y ≥ 4 , y ≤ - 4 So, the required diagram is Hence, n S 1 ∩ S 2 ∩ S 3 = 1

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