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For a complex number Z , if one root of the equation Z 2 - a Z + a = 0 is 1 + i and its other root is α , then the value of a α 4 is equal to

Options

  1. A4
  2. B- 1 2
  3. C2
  4. D- 2

Correct answer

B. - 1 2

Step-by-step solution

α + 1 + i = a α 1 + i = a α + α i = α + 1 + i ⇒ α = 1 + i i = 1 - i a = 1 - i + 1 + i = 2 α 4 = α 2 2 = 1 + - 1 - 2 i 2 = - 2 i 2 = 4 i 2 = - 4

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