If `|(z-2)//(z-3)|=2` represents a circle, then find its radius.

If z=x+i y , then the equation |(2z-i)/(z+1)|=m does not represents a circle, when m is (a) 1/2 (b). 1 (c). 2 (d). 3

The equation zbarz+(4-3i)z+(4+3i)barz+5=0 represents a circle of radius

Prove that |z-z_1|^2+|z-z_2|^2=k will represent a real circle with center ((z_1+z_2)/2) on the Argand plane if 2kgeq|z_1-z_2|^2

|z-2-3i|^2+|z-4-3i|^2=lambda represents the equation of the circle with least radius. find the value of lambda

The locus of z=x+iy satisfying |(z-i)/(z+i)|=3 then find the radious of the circle

If the complex numbers z_(1),z_(2),z_(3) represents the vertices of an equilaterla triangle such that |z_(1)|=|z_(2)|=|z_(3)| , show that z_(1)+z_(2)+z_(3)=0

If z_1,z_2,z_3 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

If |(z-z_1)/(z-z_2)|=3,w h e r ez_1a n dz_2 are fixed complex numbers and z is a variable complex number, then z lies on a (a).circle with z_1 as its interior point (b).circle with z_2 as its interior point (c).circle with z_1 as its exterior point (d).circle with z_2 as its exterior point

Let the altitudes from the vertices A, B and C of the triangle ABC meet its circumcircle at D, E and F respectively and z_1, z_2 and z_3 represent the points D, E and F respectively. If (z_3-z_1)/(z_2-z_1) is purely real then the triangle ABC is

z_1a n dz_2 are the roots of 3z^2+3z+b=0. if O(0),(z_1),(z_2) form an equilateral triangle, then find the value of bdot