If from a point P representing the complex number `z_1` on the curve `|z|=2`, two tangents are drawn from P to the curve `|z|=1`, meeting at points `Q(z_2) and R(z_3)`, then :

The points representing the complex number z for which arg((z-2)/(z+2))=pi/3 lie on

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on -

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on

Find the locus of the points representing the complex number z for which |z+5|^2-|z-5|^2=10.

A point P which represents a complex number z, moves such that |z-z_(1)|= |z-z_(2)|, then the locus of P is-

If |z-1-i|=1 , then the locus of a point represented by the complex number 5(z-i)-6 is

If z ne 1 and (z^2)/(z-1) is real then the point represented by the complex number z lies

If zne1and(z^(2))/(z-1) is real , then the point represented by the complex number z lies -

If P and Q are represented by the complex numbers z_1 and z_2 such that |1/z_2+1/z_1|=|1/(z_2)-1/z_1| , then a) O P Q(w h e r eO) is the origin of equilateral O P Q is right angled. b) the circumcenter of O P Q is 1/2(z_1+z_2) c) the circumcenter of O P Q is 1/3(z_1+z_2)

If z_1,z_2 are two non zero complex numbers such that z_1/z_2+z_2/z_1=1 then z_1,z_2 and the origin are