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

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) .

If z_(1),z_(2), z_(3) are vertices of an equilateral triangle with z_(0) its centroid, then z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=

If the complex number z_1,z_2 and z_3 represent the vertices of an equilateral triangle inscribed in the circle |z|=2 and z_1=1+isqrt(3) then (A) z_2=1,z_3=1-isqrt(3) (B) z_2=1-isqrt(3),z_3=-isqrt(3) (C) z_2=1-isqrt(3), z_3=-1+isqrt(3) (D) z_2=,z_3=1-isqrt(3)

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.

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)