If `z_0` is the circumcenter of an equilateral triangle with vertices `z_1, z_2, z_3` then `z_1^2+z_2^2+z_3^2` is equal to

If the fourth roots of unity are z_1,z_2,z_3,z_4 then z_1^2+z_2^2+z_3^2+z_4^2 is equal to

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:

If the vertices of an equilateral traingle be represented by the complex numbers z_1 , z_2 , z_3 , then prove that z_1^2+z_2^2+z_3^2=3z_0^2 and z_0 be the circumcenter of the triangle.

If A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

If z_1,z_2,z_3 are the vertices of an equilateral triangle with z_0 as its circum centre, the changing origin to z_0 new vertices become z_1',z_2',z_3' show that z_1'^2+z_2'^2+z_3'^2=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

if z_1, z_2, z_3 are the vertices pf an equilateral triangle inscribed in the circle absz=1 and z_1=i , then

If the vertices of an equilateral triangle be represented by the complex numbers z_(1),z_(2),z_(3) on the Argand diagram, then prove that, z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

Let z_1 be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_1 ne+-1 consider an equilateral triangle inscribed in the circle with z_1,z_2,z_3 as the vertices taken in the counter clockwise directtion then z_1z_2z_3 is equal to

If the complex numbers z_(1),z_(2),z_(3) represents the vertices of an equilaterla triangle such that |z_(1)|=|z_(2)|=|z_(3)| , show that z_(1)+z_(2)+z_(3)=0