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JEE Main20205 Sep 2020Evening ShiftMathematicsComplex NumberActual

The value of - 1 + i 3 1 - i 30 is :

Options

  1. A6 5
  2. B2 15 i
  3. C- 2 15
  4. D- 2 15 i

Correct answer

D. - 2 15 i

Step-by-step solution

- 1 + 3 i 1 - i 30 = 2 cos 2 π 3 + i sin 2 π 3 2 cos π 4 - i sin π 4 30 = 2 30 ( cos 20 π + i sin 20 π ) 2 15 cos 15 π 2 - i sin 15 π 2 = 2 15 ( 1 + 0 i ) ( 0 + i ) = - 2 15 i

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