Let the altitudes from the vertices A, B and Cof the triangle e ABCmeet its circumcircle at D, E and F respectively and `z_1, z_2 and z_3` represent the points D, E and F respectively. If `(z_3-z_1)/(z_2-z_1)` is purely real then the triangle ABC is

Let the altitudes from the vertices A, B and C of the triangle ABC meet its circumcircle at D, E and F respectively and z_1, z_2 and z_3 represent the points D, E and F respectively. If (z_3-z_1)/(z_2-z_1) is purely real then the triangle ABC is

The altitude form the vertices A, B and C of the triangle ABC meet its circumcircle at D,E and F, respectively . The complex number representing the points D,E, and F are z_(1),z_(2) and z_(3) , respectively. If (z_(3) -z_(1))//(z_(2) -z_(1)) is purely real, then show that triangle ABC is right-angled at A.

If z_1,z_2,z_3 are the vertices of a triangle then its centroid is

Let A, B, C, D and E be points on the complex plane, which respectively represent the complex numbers z_1,z_2,z_3, z_4 and z_5 . If (z_3 - z_2)z_4 =(z_1- z_2)z_5 , prove that the triangles ABC and DOE are similar.

Let the complex number z_1,z_2,z_3 be the vertices of an equilateral triangle . Let z_0 be the circumcentre of the triangle . Then z_1^2+z_2^2+z_3^2=

Suppose z_(1), z_(2), z_(3) represent the vertices A, B and C respectively of a Delta ABC with centroid at G. If the mid point of AG is the origin, then

If z_1, z_2, z_3 are the points A, B, C in the Argand Plane such that 1/(z_2-z_3)+1/(z_3-z_1)+1/(z_1-z_2)=0 , Prove that ABC is an equilateral triangle .