If `z_0` is the circumcenter of an equilateral triangle with vertices `z_1, z_2, z_3` then `z_1^2+z_2^2+z_3^2` is equal to

Let z_(0) be the circumcenter of an equilateral triangle whose affixes are z_(1),z_(2),z_(3) . Statement-1 : z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=3z_(0)^(2) Statement-2: z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=2(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals to : a) 3sqrt(3) b) sqrt(3) c) 3 d) 1/(3sqrt(3))

Suppose z_(1), z_(2), z_(3) are vertices of an equilateral triangle whose circumcentre -3 + 4i, then |z_(1) + z_(2) + z_(3)| is equal to

If z_1,z_2,z_3 be the vertices of an equilateral triangle, show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)= 0 or z_1^2+z_2^2+z_3^2= z_1z_2+z_2z_3+z_3z_1 .

Let the complex numbers z_1,z_2 and z_3 be the vertices of a equilateral triangle. Let z_0 be the circumcentre of the tringel ,then z_1^2+z_2^2+z_3^2= (A) z_0^2 (B) 3z_0^2 (C) 9z_0^2 (D) 0