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 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 , z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with 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.

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.

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)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)).