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NEST2022MathematicsComplex Number

Let z₁, z₂ and z₃ be three distinct complex numbers. If z₁^2+z₂^2+z₃^2=z₁ z₂+z₂ z₃+z₃ z₁ , then

Options

  1. Az₁, z₂, z₃ form the vertices of an equilateral triangle.
  2. Bz₁-z₂, z₂-z₃, z₁-z₃ form the vertices of an equilateral triangle.
  3. C(z₁-z₂ )^3+ (z₂-z₃ )^3+ (z₃-z₁ )^3 0
  4. Dz₁-z₂, z₂-z₃, z₃-z₁ are cube roots of a fixed complex number.

Correct answer

D. z₁-z₂, z₂-z₃, z₃-z₁ are cube roots of a fixed complex number.

Step-by-step solution

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