Question

What is the locus of points satisfying abs(z-z1) = abs(z-z2)) ? Note that z denotes a complex number.

Answer 1

let Z=x+iy , z1=x1+iy1 and z2=x2+iy2 where x,y are the locus pt and x1,y1, x2,y2 are constant

so abs(z-z1)=abs(z-z2)
=> (x-x1)^2 + (y-y1)^2=(x-x2)^2+(y-y2)^2
if u solve this eqn u will get following eqn
2(x1-x2)x+2(y1-y2)y=x1^2 +x2^2+y1^2+y2^2
=> mx+ny=c

where m,n & c are constant ... so it is eqn of line