The complex numbers `z_1, z_2` and the origin form an equilateral triangle only if (A) `z_1^2+z_2^2-z_1z_2=0` (B) `z_1+z_2=z_1z_2` (C) `z_1^2-z_2^2=z_1z_2` (D) none of these

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

Prove that the complex numbers z_1 and z_2 and the origin form an isosceles triangle with vertical angle 2pi//3" if " z_1^2+z_2^2+z_1z_2=0

The complex numbers z_(1) and z_(2) and the origin form an isosceles trangle with vertical angle (2 pi)/(3), then a.z_(1)^(2)+z_(2)^(2)=z_(1)z_(2)bz_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0c*z_(1)^(2)+z_(2)^(2)=3z_(1)z_(2)d none of these

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