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AP EAMCET202124 Aug 2021Evening ShiftMathematicsComplex NumberActual

What is the product of all the values of (1-i)^ 2 5 is equal to

Options

  1. A-2 i
  2. B2 i
  3. C-2
  4. D2

Correct answer

A. -2 i

Step-by-step solution

Let z=(1-i)^ 2 / 5 aligned & z= [(1-i)^2 ]^ 1 / 5 & z=(1-1-2 i)^ 1 / 5 & z=(-2 i)^ 1 / 5 z^5=-2 i z^5+2 i=0 aligned The product of all value of z is - 2 i 1 =-2 i .

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