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The solution of the equation z - z = 1 + 2 i is

Options

  1. A3 2 + 2 i
  2. B3 2 - 2 i
  3. C3 - 2 i
  4. DNone of these

Correct answer

B. 3 2 - 2 i

Step-by-step solution

Let z = x + i y Given, z - z = 1 + 2 i ⇒ x 2 + y 2 - x + i y = 1 + 2 i ⇒ x 2 + y 2 - x = 1 , y = - 2 ⇒ x 2 + 4 - x = 1 ⇒ x 2 + 4 = 1 + x 2 ⇒ 2 x = 3 ⇒ x = 3 2 ∴ z = 3 2 - 2 i

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