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

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 2z_1-3z_2 + z_3=0 , then z_1, z_2 and z_3 are represented by

If z_1, z_2, z_3 be the affixes of the vertices A, B and C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + z_2 + z_3 =

If z_1, z_2, z_3 be the affixes of the vertices A, B Mand C of a triangle having centroid at G such ;that z = 0 is the mid point of AG then 4z_1 + Z_2 + Z_3 =

Let z_1, z_2a n dz_3 represent the vertices A ,B ,a n dC of the triangle A B C , respectively, in the Argand plane, such that |z_1|=|z_2|=|z_3|=5. Prove that z_1sin2A+z_2sin2B+z_3sin2C=0.

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:

Q. Let z_1 , z_2, z_3 be three vertices of an equilateral triangle circumscribing the circle |z|=1/2 ,if z_1=1/2+sqrt3i/2 and z_1 , z_2 , z_3 are in anticlockwise sense then z_2 is

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot

Let z_1,z_2 and origin be the vertices A,B,O respectively of an isosceles triangle OAB, where OA=OB and /_AOB=2theta. If z_1, z_2 are the roots of equation z^2+z+9=0 then sec^2theta=

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