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`

Prove that the complex numbers z_1,z_2 and the origin from an isoceles triangle with vertical angle (2pi)/3 if z_1^2+z_1z_2+z_2^2=0

Prove that the complex numbers z_(1) and z_(2) and the origin form an isosceles triangle with vertical angle (2pi)/(3),ifz_(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),ifz_(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),ifz_(1)^(2)+z_(2)^(2)+z_(1)z_(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 the complex numbers z_(1) and z_(2) and the origin form an isosceles triangle with vertical angle (2pi)/(3) ,then show that z_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0.

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