P is a point on the argand diagram on the circle with OP as diameter two points taken such that `angle POQ = angle QOR = 0` 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`

P is a point on the argand diagram on the circle with OP as diameter two points taken such that /_POQ=/_QOR=0 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)^(2)cos2 theta=z_(1)z_(3)cos^(2)theta

P is any point , O being the origin. The circle on OP as diameter is drawn. Points Q and R are taken on the circle to lie on the same side of OP such that angle POQ= angle QOR=theta . If P, Q, R are z_1, z_2, z_3 such that 2 sqrt3 z_(2)^(2) = (2 + sqrt3) z_1 z_3 . Then find angle theta .

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

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?

Two points P and Q in the Argand diagram represent z and 2z+3+i. If P moves on a circle with centre at the origin and radius 4, then the locus of Q is a circle with centre

Let z_1 and z_2 be the roots of the equation 3z^2 + 3z + b=0 . If the origin, together with the points represented by z_1 and z_2 form an equilateral triangle then find the value of b.

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))