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AP EAMCET202120 Aug 2021Evening ShiftMathematicsComplex NumberActual

What is the value of ( 1 - i 3 ) 9 =

Options

  1. A2 9
  2. B- 2 9
  3. C2 9 i
  4. D- 2 9 i

Correct answer

B. - 2 9

Step-by-step solution

Given: 1 - i 3 9 = 2 9 1 - i 3 2 9 = 2 9 1 2 - i 3 2 9 = 2 9 cos π 3 - i sin π 3 9 As we know ,   cos θ ± i sin θ n =   cos n θ ± i sin n θ = 2 9 cos 3 π - isin 3 π = - 2 9

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