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JEE Main201912 Jan 2019Evening ShiftMathematicsComplex NumberActual

Let z 1 and z 2 be two complex numbers satisfying | z 1 | = 9 and | z 2 - 3 - 4 i | = 4 . Then the minimum value of z 1 - z 2 is :

Options

  1. A2
  2. B2
  3. C0
  4. D1

Correct answer

C. 0

Step-by-step solution

We have, C 1 : z 1 = 9 C 2 : z 2 - 3 - 4 i = 4 Centres of the circles are c 1 ≡ 0 , 0 and c 2 ≡ 3 , 4 . Radius of the circles are r 1 = 9 and r 2 = 4 . ⇒ c 1 c 2 = 3 2 + 4 2 = 5 and r 1 - r 2 = 5 Circles touch each other internally. ⇒ z 1 - z 2 min = 0 at the point of contact.

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