Hast du es mal mit `\draw (0,0) circle[radius=8];` versucht?
    \documentclass{article}
    \usepackage{amsmath}
    \usepackage{tikz}
    \DeclareMathOperator\real{Re}
    \DeclareMathOperator\imag{Im}
    \begin{document}
    
    \begin{tikzpicture}[x=.3cm, y=.3cm, thick]
      \draw[help lines] (-11,-10) grid[step=3mm] (11,10);
      \draw[->] (-10,0) -- (10,0) node[right] {$\real$};
      \draw[->] (0,-9) -- (0,9) node[above] {$\imag$};
      \draw (0.5,8) -- (-0.5,8) node[left] {$1$};
      \draw (0.5,-8) -- (-0.5,-8) node[left] {$-1$};
      \draw (-8,0.5) -- (-8,-0.5) node[below] {$-1$};
      \draw (8,0.5) -- (8,-0.5) node[below] {$1$};
      \draw (0,0) circle[radius=8];
    \end{tikzpicture}
    
    \end{document}
![alt text][1]
---
Man kann auch was ansehnliches mit `pgfplots` erzeugen.
    \documentclass{article}
    \usepackage{amsmath}
    \usepackage{pgfplots}
    \DeclareMathOperator\real{Re}
    \DeclareMathOperator\imag{Im}
    \begin{document}
    
    \begin{tikzpicture}
      \begin{axis}[
        axis equal,
        axis lines=middle,
        xlabel=$\real$,
        ylabel=$\imag$,
        xtick distance=1,
        ytick distance=1,
        minor tick num=7,
        grid=both,
        ]
        \addplot+[samples=80,domain=0:360,no marks] ({cos(x)},{sin(x)});
      \end{axis}
    \end{tikzpicture}
    
    \end{document}
![alt text][2]
  [1]: http://texwelt.de/wissen/upfiles/test_347.pnghttp://texwelt.de/wissen/upfiles/test_347.png
  [2]: http://texwelt.de/wissen/upfiles/test_348.png