#2_2015 Is it that complex??

Algebra Level 4

Let \({ z }_{ 1 },{ z }_{ 2 },{ z }_{ 3 }\) are the roots of \({ x }^{ 3 }+3a{ x }^{ 2 }+3bx+c=0\) in which \(a,b,c\) are complex numbers, corresponds to the points A,B,C on the complex plane. The triangle \(ABC\) is an equilateral triangle if,

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