` 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=`

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 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

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

The vertices of a square are z_1,z_2,z_3 and z_4 taken in the anticlockwise order, then z_3=

Let A(z_(1)),B(z_(2)),C(z_(3)) be the vertices of an equilateral triangle ABC in the Argand plane, then the number (z_(2)-z_(3))/(2z_(1)-z_(2)-z_(3)) , is

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot

lf z_1,z_2,z_3 are vertices of an equilateral triangle inscribed in the circle |z| = 2 and if z_1 = 1 + iotasqrt3 , then

A(z_1) , B(z_2) and C(z_3) are the vertices of triangle ABC inscribed in the circle |z|=2,internal angle bisector of angle A meets the circumcircle again at D(z_4) .Point D is:

If z_1 , z_2 ,z_3 are the vertices of an isosceles triangle right angled at z_2 , then prove that (z_1)^2+2(z_2)^2+(z_3)^2=2(z1+z3)z2

Let z_1, z_2 be two complex numbers represented by points on the circle |z_1|= and and |z_2|=2 are then