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If z 1 = 2 + 3 i , z 2 = 3 - 2 i and z 3 = - 1 - 2 3 i , then which of the following is true? (where, i 2 = - 1 )

Options

  1. Aa r g z 2 z 3 = a r g z 2 - z 1 z 3 - z 1
  2. Ba r g z 2 z 3 = a r g z 3 z 1
  3. C1 2 a r g z 2 z 3 = a r g z 2 - z 1 z 3 - z 1
  4. D2 a r g z 3 z 2 = a r g z 3 - z 1 z 2 - z 1

Correct answer

C. 1 2 a r g z 2 z 3 = a r g z 2 - z 1 z 3 - z 1

Step-by-step solution

Here, z 1 = z 1 = z 3 = 13 Hence, z 1 , z 2 , z 3 lie on a circle with center 0 , 0 and r = 13 as shown Now, a r g z 2 z 3 = 2 a r g z 2 - z 1 z 3 - z 1 ∴ a r g z 3 z 2 = 2 a r g z 3 - z 1 z 2 - z 1

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