If the points A(z), B(-z), and C(1 - z) are the vertices of an equilateral triangle ABC, then

Triangle ABC is equilateral. Hence,z2+(−z)2+(1−z)2=z(−z)+z(1−z)+(−z)(1−z)or   3z2−2z+1=−z2or   4z2−2z+1=0Sum of roots=12and      Product of roots=14