If `z_1, z_2 and z_3` are the vertices of an equilateral triangle, then `1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0`

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 .

If A(z_1), B(z_2). C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_2-2z_1)/(z_3-z_2))=pi/4 Reason(R): If /_B=alpha, then

If z_(1),z_(2),z_(3) are the vertices of an equilateral triangle,then value of (z_(2)-z_(3))^(2)+(z_(3)-z_(1))^(2)+(z_(1)-z_(2))^(2)

If A(z_(1)),B(z_(2)), C(z_(3)) are the vertices of an equilateral triangle ABC, then arg (2z_(1)-z_(2)-z_(3))/(z_(3)_z_(2))=

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))

if the complex no z_(1),z_(2) and z_(3) represents the vertices of an equilateral triangle such that |z_(1)|=|z_(2)|=|z_(3)| then relation among z_(1),z_(2) and z_(3)