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

The complex numbers z_(1), z_(2) and the origin are the vertices of an equilateral triangle in the Argand plane Prove that z_(1)^(2)+ z_(2)^(2)= z_(1).z_(2)

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 numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

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=-2,z_3=1-isqrt(3)

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

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

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

If z_1, z_2 and z_3 , are the vertices of an equilateral triangle ABC such that |z_1 -i| = |z_2 -i| = |z_3 -i| .then |z_1 +z_2+ z_3| equals: