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AP EAMCET2004MathematicsComplex Number

If z₁, z₂ are two complex numbers satisfying | z₁-3 z₂ 3-z₁ z ₂ |=1, |z₁ | 3 , then |z₂ | is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

aligned & Given that | z₁-3 z₂ 3-z₁ z ₂ |=1, |z₁ | 3 & |z₁-3 z₂ |= |3-z₁ z ₂ | [ | z₁ z₂ |= |z₁ | |z₂ | ] & |z₁-3 z₂ |^2= |3-z₁ z ₂ |^2 & (z₁-3 z₂ ) ( z ₁-3 z ₂ )= (3-z₁ z ₂ ) (3- z ₁ z₂ ) & [ z =z₂ ] & |z₁ |^2-3 z₁ z ₂-3 z₂ z ₁+9 |z₂ |^2 & =9-3 z ₁ z₂-3 z₁ z ₂+ |z₁ |^2 |z₂ |^2 & |z₁ |^2+9 |z₂ |^2-9- |z₁ |^2 |z₂ |^2=0 & (9- |z₁ |^2 ) (1- |z₂ |^2 )=0 & |z₁ |^2=9 or |z₂ |^2=1 & |z₁ |=3 or |z₂ |=1 & aligned

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