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((z_2+z_3-2z_1)/(z_3-z_2)) 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 .

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 z_1,z_2,z_3 are the vertices of a triangle then its centroid is

If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)

If z_(1),z_(2),z_(3) are the vertices of an equilateral triangle in the Argand plane, then (z_(1)^(2)+z_(2)^(2)+z_(3)^(3))=lambda(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)) holds true when :

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 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; then (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0