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The complex number z , satisfying the equation z 3 = z - and arg ⁡ z + 1 = π 4 simultaneously, is (where, i 2 = - 1 )

Options

  1. Ai
  2. B1 + 2 i
  3. C2 + 3 i
  4. D3 + 4 i

Correct answer

A. i

Step-by-step solution

z 3 = z - ⇒ z = 0 or 1 z = 0 ⇒ z = 0 z = 1 ⇒ z 4 = 1 ⇒ z = ± 1 , ± 1 Only z = i satisfies arg ⁡ z + 1 = π 4

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