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=`

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 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),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)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)).