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AP EAMCET202423 May 2024Morning ShiftMathematicsComplex NumberActual

is a complex cube root of unity and if Z is a complex number satisfying | Z -1| 2 and | ^2 Z-1- |=a , then the set of possible values of a is

Options

  1. A0 a 2
  2. B| | a 3 2 +2
  3. C1 2 a 3 2
  4. D0 a 4

Correct answer

D. 0 a 4

Step-by-step solution

aligned & Given, |Z-1| 2 and | ^2 Z-1- |=a & | ^2 Z+ ^2 |=a ( 1+ + ^2=0 ) & | ^2 ||Z+1|=a |Z-1+2|=a & |Z-1|+2 a 2+2 a & 4 a and a 0 aligned So, 0 a 4 .

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