The points `A,B,C` represent the complex numbers `z_1,z_2,z_3` respectively on a complex plane & the angle `B & C` of the triangle `ABC` are each equal to `1/2 (pi-alpha)` . If `(z_2-z_3)^2=lambda(z_3-z_1)(z_1-z_2) (sin^2) alpha/2` then determine `lambda`.

Let A, B, C represent the complex numbers z_1, z_2, z_3 respectively on the complex plane. If the circumcentre of the triangle ABC lies at the origin, then the orthocentre is represented by the complex number

Let A,B and C represent the complex number z_(1),z_(2),z_(3) respectively on the complex plane.If the circumcentre of the triangle ABC lies on the origin,then the orthocentre is represented by the number

A, B, C are the points representing the complex numbers z_1, z_2, z_3 respectively on the complex plane and the circumcentre of the triangle ABC lies at the origin. If the altitude AD of the triangle ABC meets the circumcircle again at P, then P represents the complex number

A, B, C are the point representing the complex numbers z_1,z_2,z_3 respectively on the complex plane and the circumcentre of the triangle ABC lies at the origin. If the altitude of the triangle through the vertex A meets the circumcircel again at P, then prove that P represents the complex number -(z_2z_3)/(z_1)

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 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 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))