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JEE Advanced2006MathematicsComplex NumberActual

If w= +i , where 0 and z 1 satisfies the condition that ( w- w z 1-z ) is purely real, then the set of values of z is

Options

  1. A|z|=1 and z 2
  2. B|z|=1 and z 1
  3. Cz= Z
  4. DNone of these

Correct answer

B. |z|=1 and z 1

Step-by-step solution

Let z₁= w- w _z 1-z , be purely real. array rlrl & z₁ & = z ₁ & & w- w z 1-z & = w -w z 1- z & & w-w z - w z+ w z z & = w -z w -w z +w z z & & (w- w )+( w -w)|z|^2 & =0 & & (w- w ) (1-|z|^2 ) & =0 & & |z|^2 & =1 & & |z| & =1 and z 1 . array [as, w- w 0 , since 0 ]

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