You can do it as follows. See the comments in the code for explanations:
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}[thick,font=\scriptsize]
% Axes:
% Are simply drawn using line with the `->` option to make them arrows:
% The main labels of the axes can be places using `node`s:
\draw [->] (-5,0) -- (5,0) node [above left] {$\Re\{z\}$};
\draw [->] (0,-5) -- (0,5) node [below right] {$\Im\{z\}$};
% Axes labels:
% Are drawn using small lines and labeled with `node`s. The placement can be set using options
\iffalse% Single
% If you only want a single label per axis side:
\draw (1,-3pt) -- (1,3pt) node [above] {$1$};
\draw (-1,-3pt) -- (-1,3pt) node [above] {$-1$};
\draw (-3pt,1) -- (3pt,1) node [right] {$i$};
\draw (-3pt,-1) -- (3pt,-1) node [right] {$-i$};
\else% Multiple
% If you want labels at every unit step:
\foreach \n in {-4,...,-1,1,2,...,4}{%
\draw (\n,-3pt) -- (\n,3pt) node [above] {$\n$};
\draw (-3pt,\n) -- (3pt,\n) node [right] {$\n i$};
}
\fi
\end{scope}
% The circle is drawn with `(x,y) circle (radius)`
% You can draw the outer border and fill the inner area differently.
% Here I use gray, semitransparent filling to not cover the axes below the circle
\path [draw=none,fill=gray,semitransparent] (+1,-1) circle (3);
% Place the equation into the circle:
\node [below right,gray] at (+1,-1) {$|z-1+i| \leq 3$};
\end{tikzpicture}
\end{document}
There is also the patterns
library which allows you to fill the circle with several different patterns, but personally I would prefer semi-transparent fillings.
Two examples of what you can draw with the 3d library. The first on has been modified because something was wrong with shade colour.
\documentclass[]{article}
\usepackage{tikz}
\usetikzlibrary{3d}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{5pt}%
\begin{document}
\begin{tikzpicture}
[x={(-0.2cm,-0.4cm)}, y={(1cm,0cm)}, z={(0cm,1cm)},
scale=3,
fill opacity=0.80,
color={gray},bottom color=white,top color=black]
\tikzset{zxplane/.style={canvas is zx plane at y=#1,very thin}}
\tikzset{yxplane/.style={canvas is yx plane at z=#1,very thin}}
\begin{scope}[yxplane=-1]
\shade[draw] (-1,-1) rectangle (1,1);
\draw (0,0) circle[radius=1cm] ;
\end{scope}
\begin{scope}[zxplane=-1]
\shade[draw] (-1,-1) rectangle (1,1);
\end{scope}
\begin{scope}[zxplane=1]
\shade[draw] (-1,-1) rectangle (1,1);
\end{scope}
\begin{scope}[yxplane=1]
\shade[draw] (-1,-1) rectangle (1,1);
\end{scope}
\end{tikzpicture}
\begin{tikzpicture}[scale=4]
\begin{scope}[canvas is zy plane at x=0]
\draw (0,0) circle (1cm);
\draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}
\begin{scope}[canvas is zx plane at y=0]
\draw (0,0) circle (1cm);
\draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}
\begin{scope}[canvas is xy plane at z=0]
\draw (0,0) circle (1cm);
\draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}
\end{tikzpicture}
\end{document}
Best Answer
I am wondering about the same thing as @Tarass. Here are both possibilities, a picture according to your description and a 3D picture.