Three points represented by the complex numbers a,b,c lie on a circle with centre 0 and rdius r. The tangent at C cuts the chord joining the points a,b and z. Show that `z= (a^-1+b^-1-2c^-1)/(a^-1b^1-c^2)`

If |z|=2, the points representing the complex numbers -1+5z will lie on

If |z|=1, then the point representing the complex number -1+3z will lie on a.a circle b.a parabola c.a straight line d.a hyperbola

z_(1) and z_(2), lie on a circle with centre at origin. The point of intersection of the tangents at z_(1) and z_(2) is given by

If the points represented by complex numbers z_(1)=a+ib, z_(2)=c+id " and " z_(1)-z_(2) are collinear, where i=sqrt(-1) , then

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)

Let A,B,C are 3 points on the complex plane represented by complex number a,b,c respectively such that |a|= |b|= |c|=1,a+b+c = abc=1 , then

Let z be a complex number lying oon a circle |z|=sqrt(2) a and b=b_(1)+ib_(2) (any complex number), then The equation of tangent at point 'b' is

a , b , c are three complex numbers on the unit circle |z|=1 , such that abc=a+b+c . Then |ab+bc+ca| is equal to

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

Two different non-parallel lines cut the circle |z|=r at points a,b,c and d, respectively. Prove that these lines meet at the point given by (a^(-1)+b^(-1)-c^(-1)-d^(-1))/(a^(-1)b^(-1)-c^(-1)d^(-1))