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COMEDK2016MathematicsComplex Number

The modulus and amplitude of (1+i 3 )⁸ are respectively

Options

  1. A256 and 8 3
  2. B2 and 2 3
  3. C256 and 2 3
  4. D256 and 3

Correct answer

C. 256 and 2 3

Step-by-step solution

Let z=(1+i 3 )⁸= (2 ( 1 2 + 3 2 i ) )⁸= [2 ( 60^ +i 60^ ) ]⁸= (2⁸ e^ i / 3 )⁸=2⁸ e^ 8 3 i =2⁸ e^ (2 + 2 3 ) i =2⁸ e^ 2 3 i So, modulus =2⁸=256 and amplitude = 2 3

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