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JEE Main2012MathematicsComplex NumberActual

If z 1 and z^2 z-1 is real, then the point represented by the complex number z lies

Options

  1. Aeither on the real axis or on a circle passing through the origin
  2. Bon a circle with centre at the origin
  3. Ceither on the real axis or on a circle not passing through the origin
  4. Don the imaginary axis

Correct answer

A. either on the real axis or on a circle passing through the origin

Step-by-step solution

Let z=x+ iy ( x 1 as z 1)z^2= (x^2-y^2 )+i(2 x y) z^2 z-1 is real its imaginary part =0 2 x y(x-1)-y (x^2-y^2 )=0 y (x^2+y^2-2 x )=0 y=0 ; x^2+y^2-2 x=0 z lies either on real axis or on a circle through origin.

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