Equilateral Triangle :Beware it complex

Algebra Level pending

The roots \(z_1,z_2,z_3\) of the equation \(x^3+3ax^2+3bx+c=0\) in which a,b,c are complex numbers correspond to the points A,B,C on the Guassian plane.It will be equilateral if \(a^k=b\).Find k.

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