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MHT CET202410 May 2024Morning ShiftMathematicsComplex NumberActual

If w = -1+ i 3 2 , where i = -1 , then the value of (3+w+3 w^2 )^4 is

Options

  1. A16
  2. B-16
  3. C16 w
  4. D16 w^2

Correct answer

C. 16 w

Step-by-step solution

is a complex cube root of unity array ll & =1 ...(i) & 1+ + ^2=0, & (3+ +3 ^2 )^4 ...(ii) & =(3+ +3(-1- ))^4 & =(3+ -3-3 )^4 & =(-2 )^4 & =16 ^4 & =16 ^3 & =16 array ...[from (ii)] ...[from (i)]

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