Hello, this showed up on my math test and it has everybody confused, could someone solve it ? |z-1|>|z-i|

Question

So the question is :

Solve and draw

|z-1|>|z-i|

When z= x + iy

I got to -1/2 > (x^2) + (y^2) - This is probably wrong

Thank you

Answer 1

The geometric approach is in the figure below. Point $A$ is $1$, point $B$ is $i$. The line is the set of points equidistant from the two so for your greater than sign you want the open half-plane above the line.