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 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)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 of z_(1),z_(2),z_(3) are the vertices A, B, C respectively, of on 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 number z_1, z_2 and z_3 in AP

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 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)=