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AP EAMCET201825 Apr 2018Morning ShiftMathematicsComplex NumberActual

If a = cos 8 π 11 + i sin 8 π 11 , then Re a + a 2 + a 3 + a 4 + a 5 =

Options

  1. A0
  2. B- 1 2
  3. C1 2
  4. D1

Correct answer

B. - 1 2

Step-by-step solution

We have, a = cos 8 π 11 + i sin 8 π 11 Then, a 2 = cos 8 π 11 + i sin 8 π 11 2 = cos 16 π 11 + i sin 16 π 11 a 3 = cos 24 π 11 + i sin 24 π 11 a 4 = cos 32 π 11 + i sin 32 π 11 a 5 = cos 40 π 11 + i sin 40 π 11 Now, = a + a 2 + a 3 + a 4 + a 5 = cos 8 π 11 + i sin 8 π 11 + cos 16 π 11 + i sin 16 π 11 + cos 24 π 11 + i sin 24 π 11 + cos 32 π 11 + i sin 32 π 11 + cos 40 π 11 + i sin 40 π 11 = cos 8 π 11

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