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Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

array l If z₁ z₂, z₃ are unimodular complex numbers then the greatest value of |z₁-z₂ |^2+ |z₂-z₃ |^2+ |z₃-z₁ |^2 equals to array

Correct answer

9

Step-by-step solution

aligned & |z₁-z₂ |^2+ |z₂-z₃ |^2+ |z₃-z₁ |^2 & =2 ( |z₁ |^2+ |z₂ |^2+ |z₃ |^2 )- (z₁ z ₂+ z ₁ z₂+z₂ z ₃+ z ₂ z₃+z₃ z ₁+ z ₃ z₁ ) & =6- ( z ₁ z ₂+ z ₁ z₂+z₂ z ₃+ z ₂ z₃+z₃ z ₁+ z ₃ z₁ ) aligned aligned & Now |z₁+z₂+z₃ |^2 0 & |z₁ |^2+ |z₂ |^2+ |z₃ |^2+z₁ z ₂+ z ₁ z₂+z₂ z ₃+ z ₂ z₃+z₃ z ₁+ z ₃ s ₁ 0 & - (z₁ z ₂+ z ₁ z₂+z₂ z ₃+ z ₂ z₃+z₃ z ₁+ z ₃ z₁ ) 3 aligned From (1) and (2) Maximum value =6+3=9

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