I'm having troubling understanding the answer to a question. The question is:
If $\ v=1+i$ and $\ z=x+iy$, for any real numbers x and y:
Show that the equation $\left|z-v\right|= \left|vz\right|$ represents a circle, and find its centre and radius.
The answers states:
$\ vz = (1+i)(x+iy) = (x-y) +i(x+y)$
so $\left|z-v\right|= \left|vz\right|$
becomes $\ (x-1)^2 + (y-1)^2 = (x-y)^2 + (x+y)^2$
$\ -2x - 2y +2 = x^2 + y^2 $
...
The part I don't understand is how they remove $\ i $.