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If z 1 , z 2 and z 3 are the vertices of a triangle in the argand plane such that z 1 - z 2 = z 1 - z 3 , then arg ⁡ 2 z 1 - z 2 - z 3 z 3 - z 2 is

Options

  1. Aπ 3
  2. B0
  3. Cπ 2
  4. Dπ 6

Correct answer

C. π 2

Step-by-step solution

z 1 - z 2 z 3 - z 2 = z 1 - z 2 z 3 - z 2 e i θ z 1 - z 2 z 2 - z 3 = z 1 - z 3 z 2 - z 3 e - i θ ⇒ z 1 - z 2 z 3 - z 2 + z 1 - z 3 z 3 - z 2 = purely imaginary number a r g 2 z 1 - z 2 - z 3 z 3 - z 2 = ± π 2

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