$|z-4+3i|$ = $|z-i|$
I need to describe and draw the locus. The work I have done so far is I converted the sides to their cartesian equivalents such as:
$|z-4+3i|^2$ = $|z-i|^2$
$(x-4)^2+(y+3)^2 = x^2 + (y-1)^2$
Which simplifies to:
Which is a straight line. What I am not getting is how can two sides of modulus of complex numbers simplify into a line? Is what I am doing correct at all?