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Let the complex numbers Z 1 , Z 2 and Z 3 are the vertices A , B and C respectively of an isosceles right-angled triangle A B C with right angle at C , then the value of Z 1 - Z 2 2 Z 1 - Z 3 Z 3 - Z 2 is equal to

Options

  1. A2
  2. B1
  3. C- 2
  4. D- 1

Correct answer

A. 2

Step-by-step solution

Z 1 - Z 2 Z 3 - Z 2 = 2 e i π / 4 … ( 1 ) Z 3 - Z 1 Z 2 - Z 1 = 1 2 e i π / 4 … 2 On dividing 1 by 2 , we get, Z 1 - Z 2 Z 2 - Z 1 Z 3 - Z 2 Z 3 - Z 1 = 2 ⇒ Z 1 - Z 2 2 Z 1 - Z 3 Z 3 - Z 2 = 2

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