Let `B` and `C` lie on the circle with `OA` as a diameter,where `O` is the origin. If `AOB = BOC = theta` and `z_1, z_2, z_3,` representing the points `A, B, C` respectively,then which one of the following is true?

Let z_1,z_2 be two complex numbers represented by points on the circle|z| =1 and |z|=2 respectively,then which of the following is incorrect

If z_(1),z_(2),z_(3) represents vertices A,B o* C respectively of ABC in arrtices A,B o* CAB=AC( in magnitude) then

P is a point on the argand diagram on the circle with OP as diameter two points taken such that angle POQ = angle QOR = theta . If O is the origin and P, Q, R are are represented by complex z_1, z_2, z_3 respectively then show that z_2^2cos2 theta =z_1z_3 cos^2theta

Suppose z_(1), z_(2), z_(3) represent the vertices A, B and C respectively of a Delta ABC with centroid at G. If the mid point of AG is the origin, then

Let the altitudes from the vertices A, B and C of the triangle ABC meet its circumcircle at D, E and F respectively and z_1, z_2 and z_3 represent the points D, E and F respectively. If (z_3-z_1)/(z_2-z_1) is purely real then the triangle ABC is

P is a point on the argand diagram on the circle with OP as diameter two points Q and R are taken such that angle POQ = angle QOR = theta . If O is the origin and P, Q, R are are represented by complex z_1, z_2, z_3 respectively then show that z_2^2cos2 theta =z_1z_3 cos^2theta

z_(1) and z_(2), lie on a circle with centre at origin. The point of intersection of the tangents at z_(1) and z_(2) is given by

Let A(z_(1)),B(z_(2)),C(z_(3)) be three points taken

let z1, z2,z3 be vertices of triangle ABC in an anticlockwise order and angle ACB = theta then z_2-z_3 = (CB)/(CA)(z_1-z3) e^itheta . let p point on a circle with op diameter 2 points Q & R taken on a circle such that angle POQ & QOR= theta if O be origin and PQR are complex no. z1, z2, z3 respectively then z_2/z_1 = (A) e^(itheta) cos theta (B) e^(itheta) cos 2theta (C) e^(-itheta) cos theta (D) e^(2itheta) cos 2theta

Let A(z_1),B(z_2) and C(z_3) be the three points in Argands plane The point A B and C are collinear if