The locus of the points (x,y) satisfying the relationship
|z| = 2|z-1|
is
A region exterior to a circle
or
A region interior to a circle
or
A circle
many thanks
ck
If z= x+ iy, then $\displaystyle |z|= \sqrt{x^2+ y^2}$ and $\displaystyle |z- 1|= \sqrt{(x- 1)^2+ y^2}$ so your equation says that $\displaystyle \sqrt{x^2+ y^2}= 2\sqrt{(x-1)^2+ y^2}$. Square both sides of that and reduce. What figure is that?
But with "multiple choice" you should be able to look at that equation and get the answer simply by the fact that it is and equation!