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`

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 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 2points 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_3^2/(z_1.z_2)= (A) sec^2theta.cos2theta (B) costheta.sec^2(2theta) (C) cos^2theta.sec2theta (D) sectheta.sec^2(2theta)

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 2points 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_1/z_2=

In Argand diagram, O, P, Q represent the origin, z and z+ iz respectively then angle OPQ =

In Argand diagram, O, P, Q represent the origin, z and z+ iz respectively then angle OPQ =

Line OQ is angle bisector of angle O of right angle triangle OPR , right angle at P . Point Q is such that ORQP is concyclic. If point O is orign and points P,Q,R are represented by the complex numbers z_(3),z_(2),z_(1) respectively. If (z_(2)^(2))/(z_(1)z_(2))=3/2 then ( R is circum radius of /_\OPR )

If 2z_1-3z_2 + z_3=0 , then z_1, z_2 and z_3 are represented by

If P and Q are represented by the complex numbers z_(1) and z_(2) such that |1/z_(2)+1/z_(1)|=|1/z_(2)-1/z_(1)| , then

Let z_1 and z_2 be two non - zero complex numbers such that z_1/z_2+z_2/z_1=1 then the origin and points represented by z_1 and z_2

Let z_(1),z_(2) and z_(3) be three points on |z|=1 . If theta_(1), theta_(2) and theta_(3) be the arguments of z_(1),z_(2),z_(3) respectively, then cos(theta_(1)-theta_(2))+cos(theta_(2)-theta_(3))+cos(theta_(3)-theta_(1))