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If z and w are two non-zero complex numbers such that z w = 1 and a r g z - a r g w = π 2 , then the value of 5 i z - w is equal to

Options

  1. A– 5
  2. B5 i
  3. C5
  4. D– 5 i

Correct answer

C. 5

Step-by-step solution

a r g z w = π 2 ⇒ z w = z w e i π 2 ⇒ z w = z w i ⇒ w = z w z - i ⇒ w z - = z - z w z - i ⇒ 5 i z - w = 5 - i 2 z 2 w z = 5 1 z w = 5

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