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|=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

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

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

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 z given by (a^-1+b^-1-c^-1-d^-1)/(a^-1b^-1-c^-1d^-1)

The points A,B,C represent the complex numbers z_1,z_2,z_3 respectively on a complex plane & the angle B & C of the triangle ABC are each equal to 1/2 (pi-alpha) . If (z_2-z_3)^2=lambda(z_3-z_1)(z_1-z_2) sin^2( alpha/2) then determine lambda .

Two different non-parallel lines meet the circle abs(z)=r . One of them at points a and b and the other which is tangent to the circle at c. Show that the point of intersection of two lines is (2c^(-1)-a^(-1)-b^(-1))/(c^(-2)-a^(-1)b^(-1)) .

If the point representing the complex number z_alpha is a point on or inside the circle having centre (0+i0) and radius alpha then maximum value of |z_1+z_2+……+z_n|= (A) (n(n+3))/2 (B) (n(n+1))/2 (C) (n(n-1))/2 (D) none of these

Let z_1, z_2 be two complex numbers represented by points on the circle |z_1|= and and |z_2|=2 are then