I am given the task to sketch all the points in the complex plane satisfying $ \mathrm{Re}(1/z)<1 $ I am not very good at sketching, nor seeing how to draw this in the complex plane. I was thinking that since
$ \frac{1}{z} = \frac{|z|}{z|z|} = \frac{x - iy}{x^2 + y^2} $
then $\mathrm{Re}(1/z)=x/(x^2+y^2)$. Our inequality is therefore equivalent to
$\mathrm{Re}(1/z)<1 \Leftrightarrow x < x^2 + y^2 \Leftrightarrow \left(\frac{1}{2}\right)^2 < \left( x - \frac{1}{2}\right)^2 + y^2$
So the equality represents all points in $\mathbb{R}$ that lie outside a disk of radius $1/2$ and centre $(1/2,0)$. But I have not plotted anything in the complex plane??
Any help sketching and understanding this would be greatly appreciated.