Let the complex numbers `z_1,z_2 and z_3 ` be the vertices of an equilateral triangle let `z_0` be the circumcentre of the triangle. Then prove that `z_1^2+z_2^2+z_3^2= 3z_2^2`

Let the complex numbers z_1,z_2 and z_3 be the vertices of an equilateral triangle let z_0 be the circumcentre of the triangle. Then prove that z_1^2+z_2^2+z_3^2= 3z_0^2

Let the complex numbers z_(1),z_(2) and z_(3) be the vertices of an equailateral triangle. If z_(0) is the circumcentre of the triangle , then prove that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3z_(0)^(2) .

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

If z_(1),z_(2)andz_(3) are the vertices of an equilasteral triangle with z_(0) as its circumcentre , then changing origin to z^(0) ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.