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JEE Main202523 Jan 2025Evening ShiftMathematicsComplex NumberActual

The number of complex numbers z , satisfying |z|=1 and | z z + z z |=1 , is :

Options

  1. A4
  2. B8
  3. C10
  4. D6

Correct answer

B. 8

Step-by-step solution

aligned & |z|=1 & | z z + z z |=1 & |z^2+( z )^2 |=1 aligned Let z=x+i y aligned & |(x+i y)^2+(x-i y)^2 |=1 & |2 x^2-2 y^2 |=1 & |x^2-y^2 |= 1 2 & x^2-y^2= 1 2 & and x^2+y^2=1 aligned Case I: x^2-y^2= 1 2 Case II: x^2-y^2=- 1 2

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