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JEE Advanced2007MathematicsComplex NumberActual

If |z|=1 and z 1 , then all the values of z 1-z^2 lie on

Options

  1. Aa line not passing through the origin
  2. B|z|= 2
  3. Cthe X-axis
  4. Dthe Y-axis

Correct answer

D. the Y-axis

Step-by-step solution

Let z= +i aligned z 1-z^2 & = +i 1-( 2 +i 2 ) & = +i 2 ^2 -2 i & = +i -2 i ( +i ) & = i 2 aligned Hence, z 1-z^2 lies on the imaginary axis, i.e. x=0 . ALITER Let E= z 1-z^2 = z z z -z^2 = 1 z -z which is imaginary.

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