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AP EAMCET202318 May 2023Morning ShiftMathematicsComplex NumberActual

If z is a point on the circle | z |=1 with Arg ( z )= 6 , then z¹²+1-z^6 z¹²+i z^6-1 =

Options

  1. A2+3 i
  2. B1 / 2
  3. C3+2 i
  4. D4+3 i

Correct answer

B. 1 / 2

Step-by-step solution

|z|=1 and Arg (z)= 6 aligned & z=|z| e^ i Arg (z) =i e^ i 6 =e^ 6 i & z^6=e^ i =-1 and z¹²=e^ 2 i =1 aligned Now, z¹²+1-z^6 z¹²+i z^6-1 = 1+1+1 1+i(-1)-1 = 3 -i =3 i

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