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JEE Main2004MathematicsComplex NumberActual

If |z^2-1 |=|z|^2+1 , then z lies on

Options

  1. Athe real axis
  2. Ban ellipse
  3. Ca circle
  4. Dthe imaginary axis.

Correct answer

D. the imaginary axis.

Step-by-step solution

|z^2-1 |^2= (|z|^2+1 ) (z^2-1 ) ( z ^2-1 )=|z|^4+2|z|^2+1 z^2+ z ^2+2 z z =0 z+ z =0 R(z)=0 z lies on the imaginary axis.

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