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Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

For points z₁, z₂, z₃, z₄ in complex plane such that |z₁ | 1, |z₂ |=1 and |z₃ | 1 and z₃= z₂ (z₁-z₄ ) z₁ z₄-1 . then |z_i | can be

Options

  1. A2
  2. B2 / 5
  3. C1 / 3
  4. D5 / 2

Correct answer

C. 1 / 3

Step-by-step solution

z₃= z₂ (z₁-z₄ ) z ₁ z₄-1 aligned & |z₃ |= |z₂ | |z₁-z₄ | | z ₁ z₄-1 | 1 & |z₁-z₄ | | z ₁ z₄-1 | & |z₁ |^2+ |z₄ |^2-z₁ z ₄- z₁ z₄ |z₁ |^2 |z₄ |^2- z ₁ z₄-z₁ z ₄+1 & |z₁ |^2 (1- |z₄ |^2 )- (1- |z₄ |^2 ) 0 & ( |z₁ |^2-1 ) (1- |z₄ |^2 ) 0 & 1- |z₄ |^2 0 & |z₄ | 1 ( z₁ . aligned

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