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

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) .

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 A,B and C represent the complex number z_1, z_2, z_3 respectively on the complex plane. If the circumcentre of the triangle ABC lies on the origin, then the orthocentre is represented by the number

Show that the equation of a circle passings through the origin and having intercepts a and b on real and imaginary axis, respectively, on the argand plane is Re ((z-a)/(z-ib)) = 0

The points A,B and C represent the complex numbers z_(1),z_(2),(1-i)z_(1)+iz_(2) respectively, on the complex plane (where, i=sqrt(-1) ). The /_\ABC , is

Show that the equation of a circle passing through the origin and having intercepts a and b on real and imaginary axes, respectively, on the argand plane is given by z bar z =a(R e z)+b(I mz)dot

Let A,B,C be three collinear points which are such that AB.AC=1 and the points are represented in the Argand plane by the complex numbers, 0, z_(1) and z_(2) respectively. Then,

If P represents radiation pressure , C represents the speed of light , and Q represents radiation energy striking a unit area per second , then non - zero integers x, y, z such that P^(x) Q^(y) C^(z) is dimensionless , find the values of x, y , and z .

If P represents radiation pressure , C represents the speed of light , and Q represents radiation energy striking a unit area per second , then non - zero integers x, y, z such that P^(x) Q^(y) C^(z) is dimensionless , find the values of x, y , and z .