Complex numbers `z_(1),z_(2)andz_(3)` are the vertices A,B,C respectivelt of an isosceles right angled triangle with right angle at C. show that `(z_(1)-z_(2))^(2)=2(z_1-z_(3))(z_(3)-z_(2)).`

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled trianglewith right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

Complex numbers z_1 , z_2 , z_3 are the vertices A, B, C respectively of an isosceles right angled trianglewith right angle at C and (z_1- z_2)^2 = k(z_1 - z_3) (z_3 -z_2) , then find k.

Let the complex numbers Z_(1), Z_(2) and Z_(3) are the vertices A, B and C respectively of an isosceles right - angled triangle ABC with right angle at C, then the value of ((Z_(1)-Z_(2))^(2))/((Z_(1)-Z_(3))(Z_(3)-Z_(2))) is equal to

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

Complex numbers z_(1),z_(2),z_(3) are the vertices of A,B,C respectively of an equilteral triangle. Show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

If the complex numbers z_(1),z_(2),z_(3) are in AP, then they lie on

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) .

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=2(z1+z3)z2

The complex number z_(1),z_(2),z_(3) are the vertices A, B, C of a parallelogram ABCD, then the fourth vertex D is:

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