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AP EAMCET20226 Jul 2022Evening ShiftMathematicsComplex NumberActual

If the vertices A, B and C of an isosceles A B C are respectively z₁, z₂ and z₃ and if C=90^ , then

Options

  1. A(z₁-z₂ )= (z₁-z₃ ) (z₃-z₂ )
  2. B(z₁-z₂ )^2= (z₁-z₃ ) (z₃-z₂ )
  3. C(z₁-z₂ )^2=2 (z₁-z₃ ) (z₃-z₂ )
  4. Dz₁^2+z₂^2+z₃^2=z₁ z₂ z₃+2

Correct answer

C. (z₁-z₂ )^2=2 (z₁-z₃ ) (z₃-z₂ )

Step-by-step solution

A B C is an isosceles right angled triangle with A B as hypotenuse. z₁-z₂ z₃-z₂ = 2 e^ i / 4 [Apply rotation about a point B ] aligned & z₂-z₁ z₃-z₁ = 2 e^ - i 4 & [Apply rotation about a point A ] & ( z₁-z₂ z₃-z₂ ) ( z₂-z₁ z₃-z₁ )=2 & (z₁-z₂ ) (z₁-z₂ ) (z₃-z₂ ) (z₁-z₃ ) =2 & (z₁-z₂ )^2=2 (z₁-z₃ ) (z₃-z₂ ) aligned

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