The points `A(z_1), B(z_2) and C(z_3)` form an isosceles triangle in the Argand plane right angled at B, then `(z_1-z_2)/(z_3-z_2)` can be (A) 1 (B) -1 (C) `-i` (D) none of these

If A(z_(1)),B(z_(2)), C(z_(3)) are the vertices of an equilateral triangle ABC, then arg (2z_(1)-z_(2)-z_(3))/(z_(3)_z_(2))=

If A(z_(1)),B(z_(2)) and C(z_(3)) are three points in the Argand plane such that z_(1)+omegaz_(2)+omega^(2)z_(3)=0 , then

Let A(z_(1)),B(z_(2)),C(z_(3)) be the vertices of an equilateral triangle ABC in the Argand plane, then the number (z_(2)-z_(3))/(2z_(1)-z_(2)-z_(3)) , is

If A(z_1), B(z_2). C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_2-2z_1)/(z_3-z_2))=pi/4 Reason(R): If /_B=alpha, then

Let A(z_1),B(z_2) and C(z_3) be the vertices of an equilateral triangle in the Argand plane such that |z_1|=|z_2|=|z_3|. Then (A) (z_2+z_3)/(2z_1-z_2-z_3) is purely real (B) (z_2-z_3)/(2z_1-z_2-z_3) is purely imaginary (C) |arg(z_1/z_2)|=2 arg((z_3-z_2)/(z_1-z_2))| (D) none of these

If z_(1), z_(2) and z_(3) are the vertices of a triangle in the argand plane such that |z_(1)-z_(2)|=|z_(1)-z_(3)| , then |arg((2z_(1)-z_(2)-z_(3))/(z_(3)-z_(2)))| is

If z_(1),z_(2),z_(3) are the vertices of an isosceles triangle right angled at z_(2), then prove that (z_(1))^(2)+2(z_(2))^(2)+(z_(3))^(2)=