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 angleOPQ=

In the Argand diagram. if O, P and Q represent respectively the origin and the complex numbers z and z+iz, then the angle angle OPQ is :

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

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

Let z,z_(0) be two complex numbers. It is given that abs(z)=1 and the numbers z,z_(0),zbar_(0),1 and 0 are represented in an Argand diagram by the points P, P_(0) ,Q,A and the origin, respectively. Show that /_\POP_(0) and /_\AOQ are congruent. Hence, or otherwise, prove that abs(z-z_(0))=abs(zbar(z_(0))-1)=abs(zbar(z_(0))-1) .

Let z,z_(0) be two complex numbers. It is given that abs(z)=1 and the numbers z,z_(0),zbar_(0),1 and 0 are represented in an Argand diagram by the points P, P_(0) ,Q,A and the origin, respectively. Show that /_\POP_(0) and /_\AOQ are congruent. Hence, or otherwise, prove that abs(z-z_(0))=abs(zbar(z_(0))-1)=abs(zbar(z_(0))-1) .

Let z,z_(0) be two complex numbers. It is given that abs(z)=1 and the numbers z,z_(0),zbar_(0),1 and 0 are represented in an Argand diagram by the points P, P_(0) ,Q,A and the origin, respectively. Show that /_\POP_(0) and /_\AOQ are congruent. Hence, or otherwise, prove that abs(z-z_(0))=abs(zbar(z_(0))-1)=abs(zbar(z_(0))-1) .

Let z,z_(0) be two complex numbers. It is given that abs(z)=1 and the numbers z,z_(0),bar(z_(0)),1 and 0 are represented in an Argand diagram by the points P,P_(0),Q,A and the origin, respectively. Show that /_\POP_(0) and /_\AOQ are congruent. Hence, or otherwise, prove that abs(z-z_(0))=abs(zbar(z_(0))-1) .

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