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 /_OPQ=

Letz,z_0be two complex numbers z_0being the cojugate of z_0. The numbers z, z_0, zbar z_0,1 and 0 are represented in argand diagram by P,P_0, Q, A and origin respectively. If |z|=1, then (A) triangle POP_0 and triangle AOQ are congruent (B) |z-z_0| = |zbarz_0 -1| (C) |z-z_0| = 1/2|zbarz_0 -1| (D)none of these

Let OP.OQ=1 and let O,P and Q be three collinear points. If O and Q represent the complex numbers of origin and z respectively, then P represents

The complex numbers z_1=2+5i , z_2=3-4i and z_3=-4+i are represented by the points A, B and C respectively on an Argand diagram. Sketch the Argand diagram

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),z_(2) and z_(3) represent the vertices A,B, and C of the triangle ABC , respectively,in the Argand plane,such that |z_(1)|=|z_(2)|=|z_(3)|=5. Prove that z_(1)sin2A+z_(2)sin2B+z_(3)sin2C=0

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

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)