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
- A2
- B2 / 5
- C1 / 3
- 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