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BITSAT2021MathematicsComplex NumberActual

If z is a complex number such that z²=( z )² , then

Options

  1. Az is purely real
  2. Bz is purely imaginary
  3. Ceither z is purely real or purely imaginary
  4. DNone of these

Correct answer

C. either z is purely real or purely imaginary

Step-by-step solution

Let z=x+i y , then its conjugate z =x-i y Given that z²=( z )² array l x²-y²+2 i x y=x²-y²-2 i x y 4 i x y=0 array

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