How can I do these contour graphs using TikZ?

Question

It would be very helpful for me if you could help me create these images with TikZ. With this I could make more than I have. Thank you

Answer 1

This site is meant to give users information that allows them to achieve what they want on their own. You will see that it is much more fun if you can do these things yourself instead having to ask others for help. How can one fill a contour? Unsurprisingly, by adding fill=<color>.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{amsmath}
% from https://tex.stackexchange.com/a/430239/121799
\usetikzlibrary{arrows.meta,bending,decorations.markings,hobby,patterns,calc}
\tikzset{% inspired by https://tex.stackexchange.com/a/316050/121799
    arc arrow/.style args={%
    to pos #1 with length #2}{
    decoration={
        markings,
         mark=at position 0 with {\pgfextra{%
         \pgfmathsetmacro{\tmpArrowTime}{#2/(\pgfdecoratedpathlength)}
         \xdef\tmpArrowTime{\tmpArrowTime}}},
        mark=at position {#1-\tmpArrowTime} with {\coordinate(@1);},
        mark=at position {#1-2*\tmpArrowTime/3} with {\coordinate(@2);},
        mark=at position {#1-\tmpArrowTime/3} with {\coordinate(@3);},
        mark=at position {#1} with {\coordinate(@4);
        \draw[-{Latex[length=#2,bend]}]       
        (@1) .. controls (@2) and (@3) .. (@4);},
        },
     postaction=decorate,
     },
fixed arc arrow/.style={arc arrow=to pos #1 with length 2mm}     
}
% from https://tex.stackexchange.com/a/29367/121799
\tikzset{
        hatch distance/.store in=\hatchdistance,
        hatch distance=10pt,
        hatch thickness/.store in=\hatchthickness,
        hatch thickness=2pt
    }
\makeatletter
\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{flexible hatch}
{\pgfqpoint{0pt}{0pt}}
{\pgfqpoint{\hatchdistance}{\hatchdistance}}
{\pgfpoint{\hatchdistance-1pt}{\hatchdistance-1pt}}%
{
    \pgfsetcolor{\tikz@pattern@color}
    \pgfsetlinewidth{\hatchthickness}
    \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
    \pgfpathlineto{\pgfqpoint{\hatchdistance}{\hatchdistance}}
    \pgfusepath{stroke}
}
\makeatother
\begin{document}
\begin{tikzpicture}[closed hobby,scale=1.5]
\path[fill=gray,postaction={decorate,decoration={markings,
mark=at position 0.8 with {\node at (0,-6pt) {$\gamma$};},
mark=at position 0.85 with {\coordinate (X) at (0,6pt);}}}]
plot coordinates { 
(90:0.8) (135:1.2) (180:1.5) (225:1.6) (270:0.8) (315:1.15) (0:1.4)
(45:1.3)};
\draw[thick,fixed arc arrow/.list={1/4,3/4}] plot coordinates { 
(90:0.8) (135:1.2) (180:1.5) (225:1.6) (270:0.8) (315:1.15) (0:1.4)
(45:1.3)};
\draw[latex-] (X) -- ++ (0.6,0.3) node[right,align=center] {$f$ analytic\\ 
here};
\node at (0,0) {$A=\text{inside of}~\gamma$};
\begin{scope}[yshift=-3cm]
\draw[thick,rotate=25] plot coordinates { 
(90:1) (135:1.5) (180:2.5) (225:1.6) (270:1) (315:1.5) (0:2.5)
(45:1.5)};
\filldraw[pattern=flexible hatch,hatch distance=10pt,hatch thickness=0.6pt,dashed] 
(-1,-0.5) coordinate(z0) circle (1);
\node[inner sep=1.5pt,circle,fill,label=right:$z_0$] at (z0){};
\node[inner sep=1.5pt,circle,fill,label=right:$z_1$] (z1) at ($(z0)+(25:1.5)$){};
\node[inner sep=1.5pt,circle,fill,label=right:$z_2$] (z2) at ($(z0)+(-25:0.5)$){};
\node[inner sep=1.5pt,circle,fill,label=right:$z_3$] (z3) at ($(z0)+(25:0.5)$){};
\node[inner sep=1.5pt,circle,fill,label=right:$z_n$] (zn) at ($(z0)+(90:0.5)$){};
\draw[-latex] (z0) -- ++ (120:1) node[right,yshift=-4pt,xshift=2pt]{$r$};
\draw[latex-] ($(z0)+(0,-0.3)$) to[out=-60,in=180] ++(0.5,-1) 
node[right]{$h(z)=0~\forall z\in D(z_0,r)$};
\end{scope}
\end{tikzpicture}
\end{document} 

As I can see from your figures, you seem to understand complex analysis. Believe me, TikZ is easier than that, and it is always fun to learn some new tricks. So please, before asking another question, try yourself, and if you get stuck, post the code that you have tried, and I am sure you will get great support.