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

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

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)

The points A,B and C represent the complex numbers z_(1),z_(2),(1-i)z_(1)+iz_(2) respectively, on the complex plane (where, i=sqrt(-1) ). The /_\ABC , is

Represent the complex number z=1+isqrt3 in polar form.

If A and B represent the complex numbers z_(1) and z_(2) such that |z_(1)+z_(2)|=|z_(1)-z_(2)| , then the circumcenter of triangleOAB , where O is the origin, is

Represent the complex number z=1+i sqrt(3) in the polar form.

If the complex numbers z_1, z_2, z_3, z_4 taken in that order, represent the vertices of a rhombus, then

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 .