As stated in the question I am asked to sketch or graph the area $ \left| z - \frac{1}{2}\right|\leq\frac{1}{2} $ Now in the $z$ plane this is all complex numbers that is less than $1/2$ away from the real number $1/2$
My problem is sketching the region in the $\omega=1/z$. I think it becomes a rectangle, but I am not able to prove it.
Any nudges or hints would be greatly appreciated.