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JEE Main20198 Apr 2019Evening ShiftMathematicsComplex NumberActual

If z = 3 2 + i 2 i = - 1 , then 1 + i z + z 5 + i z 8 9 is equal to:

Options

  1. A- 1
  2. B1
  3. C0
  4. D- 1 + 2 i 9

Correct answer

A. - 1

Step-by-step solution

z = 3 2 + i 2 ∴ i z = - 1 2 + 3 2 i = ω ∴ 1 + i z + z 5 + i z 8 9 = 1 + ω + ω 5 i 5 + i × ω 8 i 8 9 = 1 + ω - i ω 2 + i ω 2 9 = - ω 2 9 = - ω 18 = - 1

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