How can we represent set $S= \{z:|z|>|z-1|\}$ graphically.

Question

Here I have plotted graph of $|z|$ and $|z-1|$ but I am not getting the required condition. I have to plot this using divs in a plane for which general set is $\{z:|z-z_0|<r\}$ where $r$ is radius centered at $z_0$.

Answer 1

Your condition reads: the distance from $z$ to the origin is greater than the distance to the real number $1$. If you draw the bisector of the segment joining $0$ and $1$, your region is the right half-plane.

Answer 2

$|z| > |z-1|$ basically translates to, "Find the points $z$ such that the distance from $z$ to the origin is greater than the distance between $z$ & $1$". This is what the graph looks like, please pretend the $y$-axis is the complex axis.