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AP EAMCET202315 May 2023Evening ShiftMathematicsComplex NumberActual

The product of the four values of (1+i 3 )^ 3 / 4 is

Options

  1. A-8 i
  2. Bi
  3. C-8
  4. D8

Correct answer

D. 8

Step-by-step solution

Let z=(1+i 3 )^ 3 / 4 Product of four values of z=|z|^4...(i) Now, z=2^ 3 / 4 ( 1 2 +i 3 2 )^ 3 / 4 aligned & z=2^ 3 / 4 (e^ .i 3 )^ 3 / 4 =2^ 3 / 4 e^ i 4 . & |z|=2^ 3 / 4 |e^ i 4 | & |z|=2^ 3 / 4 1=2^ 3 / 4 & |z|^4=2^3=8 aligned Product of four values of z=8 .

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