#2_2015 Is it that complex??

Algebra Level 4

Let z1,z2,z3{ z }_{ 1 },{ z }_{ 2 },{ z }_{ 3 } are the roots of x3+3ax2+3bx+c=0{ x }^{ 3 }+3a{ x }^{ 2 }+3bx+c=0 in which a,b,ca,b,c are complex numbers, corresponds to the points A,B,C on the complex plane. The triangle ABCABC is an equilateral triangle if,

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