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I would like to draw the set of points in the complex plane that satisfies $|z-1+i| <= 3$ using LaTeX (with TikZ, or some related system). I would want to fill this circle with say dashed lines, or something of the sort, so that it's not "completely" filled. I would also want the axis labeled. I have no idea on how to do this properly, unfortunately. Could anyone tell me how, or supply me with some reference? Would be perfect.

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up vote 16 down vote accepted

You can do it as follows. See the comments in the code for explanations:

    % 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] {$\n i$};
    % 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) {$|z-1+i| \leq 3$};


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.

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@Jasper: That's correct. I added that labels at the very end and didn't thought about that. – Martin Scharrer May 15 '11 at 18:00
@MartinScharrer: Very nice! I added your example to the TikZ gallery: A circle in the complex plane Is this ok for you? – Stefan Kottwitz Jan 6 '12 at 23:00



enter image description here

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true, but I defined the equation as y=Re(x)+Im(x) ... :-)) – Herbert May 15 '11 at 18:15

You could use the PGFPlots package for this. By using the option disabledatascaling, you can draw objects using \node and \draw and the like with the axis coordinates:


    axis equal,
    axis lines=middle,

\fill [opacity=0.3] (1,-1) circle [radius=3];

circle in complex plane

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@Jasper: Good point! – Jake May 15 '11 at 18:02

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