A simple (indented) integration contour with Tikz

Question

I would like to draw an integration contour which is pretty easy I think, but I am a newbie at the Tikz package. The integration contour goes from

-iinfinity to +iinfinity

parallel to the Imaginary axis but not exactly on it, rather slightly to the left (or right) of it. The integration contour also has a semicircle on it somewhere near the origin but not exactly on the origin.

I guess I'm looking for an indented contour but not the usual ones where one go from -infinity to + infinity with a jump over a pole as in the following picture but like I said I would like it to go vertically.

I also found this picture, I want something very close to this. If I get some help getting what is in the picture in the link I think I can manage doing the rest myself.

indented integration contour

Please, any help would be appreciated, thanks.

Answer 1

Here is a first approximation, based on the answer to the question Drawing complex integration.

Is this close to what you want?

\documentclass{article}
\usepackage{tikz}
\begin{document}
\usetikzlibrary{calc,decorations.markings}

\begin{tikzpicture}
\draw (0,-5.5) -- (0,5.5);  % Axis
\draw (-5.5,0) -- (5.5,0);   
\foreach \y in {-5,...,5} {
  \draw (-4pt,\y) -- (4pt,\y) node[pos=0,left] {\y};
  \draw (\y,-4pt) -- (\y,4pt) node[pos=0,below] {\y};
}

\node at (0,-1.5) {$\times$}; % Pole

% Contour line
\draw[thick,red,xshift=2pt,
decoration={ markings,  % This schema allows for fine-tuning the positions of arrows
      mark=at position 0.2 with {\arrow{latex}}, 
      mark=at position 0.6 with {\arrow{latex}},
      mark=at position 0.8 with {\arrow{latex}}, 
      mark=at position 0.98 with {\arrow{latex}}}, 
      postaction={decorate}]
  (0,-5) -- (0,-1.7) arc (-90:90:.2) -- (0,5);
\draw[thick,red,xshift=2pt,
decoration={ markings,
      mark=at position 0.2 with {\arrow{latex}}, 
      mark=at position 0.4 with {\arrow{latex}},
      mark=at position 0.6 with {\arrow{latex}}, 
      mark=at position 0.8 with {\arrow{latex}}}, 
      postaction={decorate}]
 (0,5) arc (90:-90:5) -- (0,-5);
\end{tikzpicture}
\end{document}