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Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

Consider the set of complex number A, B, C and S defined as aligned & A= z:|| z+2|-| z-2||=2 & B= z: ( z-1 z )= 2 & C= z: (z-1)= & S= z: Re ( z-1 z+1 )=0 aligned If z₁, z₂, z₃ S , then find the minimum value of |z₁+z₂ |^2+ |z₂+z₃ |^2+ |z₃+z₁ |^2 .

Correct answer

3

Step-by-step solution

A, B and C represented geometrically as clear A B C= Clearly S represents the set of complex number lying on the circle |z|=1, z -1 aligned & |z₁+z₂ |^2+ |z₂+z₃ |^2+ |z₃+z₁ |^2=3+ (z₁+z₂+z₃ ) & =3+ |z₁+z₂+z₃ |^2 3 aligned

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