Let $z_1, z_2$ and $z_3$ be three distinct complex numbers. If $z_1^2+z_2^2+z_3^2=z_1 z_2+z_2 z_3+z_3 z_1$, then

• Correct answer
  A

  $z_1, z_2, z_3$ form the vertices of an equilateral triangle.
• B

  $z_1-z_2, z_2-z_3, z_1-z_3$ form the vertices of an equilateral triangle.
• Correct answer
  C

  $\left(z_1-z_2\right)^3+\left(z_2-z_3\right)^3+\left(z_3-z_1\right)^3 \neq 0$
• Correct answer
  D

  $z_1-z_2, z_2-z_3, z_3-z_1$ are cube roots of a fixed complex number.

Hence, the correct answer is options: 'A', 'C', 'D'.