How to plot polar formed complex numbers?

I would like to draw the figure below in LaTeX and am having a bit of a difficulty. How can I do it?

%\usepackage[dvips,pdftex]{graphicx}

\documentclass[a4paper,12pt]{article}%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{indentfirst}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{color}
\usepackage[dvips]{epsfig}
\usepackage[dvips]{graphicx}
\usepackage{float}
\usepackage[latin1]{inputenc}
\usepackage[brazil]{babel}
\usepackage{tikz}
\usepackage{multicol}
\usepackage{cancel}
{hyperref}%
\setcounter{MaxMatrixCols}{30}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=5.50.0.2953}
%TCIDATA{LastRevised=Thursday, March 14, 2019 23:50:47}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
%TCIDATA{BibliographyScheme=Manual}
%BeginMSIPreambleData
\providecommand{\U}[1]{\protect\rule{.1in}{.1in}}
%EndMSIPreambleData
\setlength{\topmargin}{-1.5cm} \setlength{\oddsidemargin}{0.0cm}
\setlength{\evensidemargin}{0.0cm} \setlength{\textheight}{24cm}
\setlength{\textwidth}{16.5cm}
\renewcommand{\baselinestretch}{1.25}
\begin{document}
\begin{titlepage}

\begin{center}
%\tiny,\small,\large,\Large,\LARGE, \huge,\Huge,\HUGE
{ \Large \sc Universidade Federal do Maranhão}
\vskip 0.5cm
{ \Large \sc Centro de Ciências Exatas e Tecnologia}
\vskip 0.5cm {\Large \sc Matheus Rodrigues Linhares Guimarães}
\vskip 3 cm {\LARGE \sc \textbf{VARIÁVEIS COMPLEXAS}}
\begin{figure}[H]
\centering
$\includegraphics[width=100mm]{./Figuras/capa5.png}$
\end{figure}

\vskip 2cm
\vfill
{\sc 2019.1}
\end{center}
\end{titlepage}%

\end{document}


After doing the code, how do I put it in place of \ begin {figure} [H] \ centering \ [ \ includegraphics [width = 100mm] {./ Figures / layer5.png} ] \ end {figure} so you do not need figures?

• This question could benefit from a textual description of what you are trying to achieve. That way, when somebody wants to do something similar, searching for those terms will help them find this question and it's answer. Specifically, mention the part(s) of the diagram which are not being drawn to your desire. Something like "How to draw concentric circles" or "How to draw a line segment whose endpoint lies on the edge of a circle" or whatever you feel best describes the part you can't draw in your image. This will also help your question from seeming too broad. – Davy M Mar 16 at 20:00
• @Davy M So how can I do it? I put this in the description of the question? – Matheus Guimaraes Mar 17 at 0:37
• @MatheusGuimaraes Yes, I would add it after you mention that you are having a bit of difficulty, a more exact description of what parts are giving you difficulty. This probably isn't a priority since you already got your answer, but it will likely help other people who want to do something similar so they can find your question and the answer. – Davy M Mar 17 at 1:44

Note: The codes are arranged in "quality-increasing" order in my opinion, i.e. the best one is the last one.

Like this?

\documentclass[tikz]{standalone}
\usetikzlibrary{quotes,angles}
\begin{document}
\begin{tikzpicture}
\draw (0,-4)--(0,4) node[above] {$Im$} (-4,0)--(4,0) node[right] {$Re$};
\draw[dashed] (0,0) circle (3) circle (2);
\coordinate (a) at (80:3);
\coordinate (b) at (3,0);
\coordinate (m) at (25:2);
\coordinate (n) at (-95:2);
\coordinate (p) at (145:2);
\coordinate (o) at (0,0);
\fill[black] (a) circle (2pt) (b) circle (2pt) (m) circle (2pt) (n) circle (2pt) (p) circle (2pt) (2,0) circle (2pt);
\draw (a) node[above right] {$z=|z|e^{i\theta}$};
\draw (b) node[below] {$|z|$};
\draw (2,0) node[below] {$|z|^{1/3}$};
\draw (m) node[right] {$|z|^{1/3}e^{i\theta/3}$};
\draw (n) node[below] {$|z|^{1/3}e^{i(\theta+4\pi)/3}$};
\draw (p) node[above] {$|z|^{1/3}e^{i(\theta+2\pi)/3}$};
\draw (.1,1.5)--(0,1.5) node[left] {$i$};
\draw (1.5,.1)--(1.5,0) node[below] {$1$};
\draw (0,0)--(a) (0,0)--(m) (0,0)--(n) (0,0)--(p);
\draw[dashed] (m)--(n)--(p)--cycle;
\pic[draw,dashed,thick,"$\theta$",angle radius=0.8cm,angle eccentricity=1.3] {angle=b--o--a};
\end{tikzpicture}
\end{document}


Improved version:

\documentclass[tikz]{standalone}
\usetikzlibrary{quotes,angles,positioning}
\begin{document}
\begin{tikzpicture}
\begin{scope}[every node/.style={fill=white,inner sep=2pt}]
\draw (0,-4)--(0,4) node[above] {$Im$} (-4,0)--(4,0) node[right] {$Re$};
\draw[dashed] (0,0) circle (3) circle (2);
\coordinate (a) at (80:3);
\coordinate (b) at (3,0);
\coordinate (m) at (25:2);
\coordinate (n) at (-95:2);
\coordinate (p) at (145:2);
\coordinate (o) at (0,0);
\draw (a) node[above right] {$z=|z|e^{i\theta}$};
\draw (b) node[below right] {$|z|$};
\draw (2,0) node[below left=0cm and -2em] {$|z|^{1/3}$};
\draw (m) node[right] {$|z|^{1/3}e^{i\theta/3}$};
\draw (n) node[below] {$|z|^{1/3}e^{i(\theta+4\pi)/3}$};
\draw (p) node[above] {$|z|^{1/3}e^{i(\theta+2\pi)/3}$};
\draw (.1,1.5)--(0,1.5) node[left] {$i$};
\draw (1.5,.1)--(1.5,0) node[below] {$1$};
\draw (0,0)--(a) (0,0)--(m) (0,0)--(n) (0,0)--(p);
\draw[dashed] (m)--(n)--(p)--cycle;
\end{scope}
\pic[draw,dashed,thick,"$\theta$",angle radius=0.8cm,angle eccentricity=1.3] {angle=b--o--a};
\fill[black] (a) circle (2pt) (b) circle (2pt) (m) circle (2pt) (n) circle (2pt) (p) circle (2pt) (2,0) circle (2pt);
\end{tikzpicture}
\end{document}


Thanks to @marmot, I think this figure is more mathematically true ;-)

\documentclass[tikz]{standalone}
\usetikzlibrary{quotes,angles,positioning}
\begin{document}
\begin{tikzpicture}
\begin{scope}[every node/.style={fill=white,inner sep=2pt}]
\draw (0,-4)--(0,4) node[above] {$Im$} (-4,0)--(4,0) node[right] {$Re$};
\draw[dashed] (0,0) circle (3) circle (2);
\coordinate (a) at (80:3);
\coordinate (b) at (3,0);
\coordinate (m) at (80/3:2);
\coordinate (n) at ({80/3-120}:2);
\coordinate (p) at ({80/3+120}:2);
\coordinate (o) at (0,0);
\draw (a) node[above right] {$z=|z|e^{i\theta}$};
\draw (b) node[below right] {$|z|$};
\draw (2,0) node[below left=0cm and -2em] {$|z|^{1/3}$};
\draw (m) node[right] {$|z|^{1/3}e^{i\theta/3}$};
\draw (n) node[below] {$|z|^{1/3}e^{i(\theta+4\pi)/3}$};
\draw (p) node[above] {$|z|^{1/3}e^{i(\theta+2\pi)/3}$};
\draw (.1,1.5)--(0,1.5) node[left] {$i$};
\draw (1.5,.1)--(1.5,0) node[below] {$1$};
\draw (0,0)--(a) (0,0)--(m) (0,0)--(n) (0,0)--(p);
\draw[dashed] (m)--(n)--(p)--cycle;
\end{scope}
\pic[draw,dashed,thick,"$\theta$",angle radius=0.8cm,angle eccentricity=1.3] {angle=b--o--a};
\fill[black] (a) circle (2pt) (b) circle (2pt) (m) circle (2pt) (n) circle (2pt) (p) circle (2pt) (2,0) circle (2pt);
\end{tikzpicture}
\end{document}


Another choice: \Im instead of Im and \Re instead of Re (@Sebastiano's request):

\documentclass[tikz]{standalone}
\usetikzlibrary{quotes,angles,positioning}
\begin{document}
\begin{tikzpicture}
\begin{scope}[every node/.style={fill=white,inner sep=2pt}]
\draw (0,-4)--(0,4) node[above] {$\Im$} (-4,0)--(4,0) node[right] {$\Re$};
\draw[dashed] (0,0) circle (3) circle (2);
\coordinate (a) at (80:3);
\coordinate (b) at (3,0);
\coordinate (m) at (80/3:2);
\coordinate (n) at ({80/3-120}:2);
\coordinate (p) at ({80/3+120}:2);
\coordinate (o) at (0,0);
\draw (a) node[above right] {$z=|z|e^{i\theta}$};
\draw (b) node[below right] {$|z|$};
\draw (2,0) node[below left=0cm and -2em] {$|z|^{1/3}$};
\draw (m) node[right] {$|z|^{1/3}e^{i\theta/3}$};
\draw (n) node[below] {$|z|^{1/3}e^{i(\theta+4\pi)/3}$};
\draw (p) node[above] {$|z|^{1/3}e^{i(\theta+2\pi)/3}$};
\draw (.1,1.5)--(0,1.5) node[left] {$i$};
\draw (1.5,.1)--(1.5,0) node[below] {$1$};
\draw (0,0)--(a) (0,0)--(m) (0,0)--(n) (0,0)--(p);
\draw[dashed] (m)--(n)--(p)--cycle;
\end{scope}
\pic[draw,dashed,thick,"$\theta$",angle radius=0.8cm,angle eccentricity=1.3] {angle=b--o--a};
\fill[black] (a) circle (2pt) (b) circle (2pt) (m) circle (2pt) (n) circle (2pt) (p) circle (2pt) (2,0) circle (2pt);
\end{tikzpicture}
\end{document}


Thanks to @JasperHabicht in this answer, now I can optimize the separating space between node texts and the line:

\documentclass[tikz]{standalone}
\usetikzlibrary{quotes,angles,positioning}
\usepackage[outline]{contour}
\contourlength{2pt}
\begin{document}
\begin{tikzpicture}
\draw (0,-4)--(0,4) node[above] {$\Im$} (-4,0)--(4,0) node[right] {$\Re$};
\draw[dashed] (0,0) circle (3) circle (2);
\coordinate (a) at (80:3);
\coordinate (b) at (3,0);
\coordinate (m) at (80/3:2);
\coordinate (n) at ({80/3-120}:2);
\coordinate (p) at ({80/3+120}:2);
\coordinate (o) at (0,0);
\draw (a) node[above right] {\contour{white}{$z=|z|e^{i\theta}$}};
\draw (b) node[below right] {\contour{white}{$|z|$}};
\draw (2,0) node[below left=0cm and -2em] {\contour{white}{$|z|^{1/3}$}};
\draw (m) node[right] {\contour{white}{$|z|^{1/3}e^{i\theta/3}$}};
\draw (n) node[below] {\contour{white}{$|z|^{1/3}e^{i(\theta+4\pi)/3}$}};
\draw (p) node[above] {\contour{white}{$|z|^{1/3}e^{i(\theta+2\pi)/3}$}};
\draw (.1,1.5)--(0,1.5) node[left] {\contour{white}{$i$}};
\draw (1.5,.1)--(1.5,0) node[below] {\contour{white}{$1$}};
\draw (0,0)--(a) (0,0)--(m) (0,0)--(n) (0,0)--(p);
\draw[dashed] (m)--(n)--(p)--cycle;
\pic[draw,dashed,thick,"$\theta$",angle radius=0.8cm,angle eccentricity=1.3] {angle=b--o--a};
\fill[black] (a) circle (2pt) (b) circle (2pt) (m) circle (2pt) (n) circle (2pt) (p) circle (2pt) (2,0) circle (2pt);
\end{tikzpicture}
\end{document}


Your code is not compilable because of a conflict (?) between babel and quotes (I don't know if it is true).

We can fix it by not using quotes anymore:

%\usepackage[dvips,pdftex]{graphicx}

\documentclass[a4paper,12pt]{article}%
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{indentfirst}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{color}
\usepackage[dvips]{epsfig}
\usepackage[dvips]{graphicx}
\usepackage{float}
\usepackage[latin1]{inputenc}
\usepackage[brazil]{babel}
\usepackage{tikz}
\usepackage{multicol}
\usepackage{cancel}
{hyperref}%
\setcounter{MaxMatrixCols}{30}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=5.50.0.2953}
%TCIDATA{LastRevised=Thursday, March 14, 2019 23:50:47}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
%TCIDATA{BibliographyScheme=Manual}
%BeginMSIPreambleData
\providecommand{\U}[1]{\protect\rule{.1in}{.1in}}
%EndMSIPreambleData
\setlength{\topmargin}{-1.5cm} \setlength{\oddsidemargin}{0.0cm}
\setlength{\evensidemargin}{0.0cm} \setlength{\textheight}{24cm}
\setlength{\textwidth}{16.5cm}
\renewcommand{\baselinestretch}{1.25}
\usetikzlibrary{angles,positioning}
\begin{document}
\begin{titlepage}
\vspace{1cm}
\begin{center}
%\tiny,\small,\large,\Large,\LARGE, \huge,\Huge,\HUGE
{ \Large \sc Universidade Federal do Maranhão}
\vskip 0.5cm
{ \Large \sc Centro de Ciências Exatas e Tecnologia}
\vskip 0.5cm {\Large \sc Matheus Rodrigues Linhares Guimarães}
\vskip 3 cm {\LARGE \sc \textbf{VARIAVEIS COMPLEXAS}}

\begin{center}
\begin{tikzpicture}
\begin{scope}[every node/.style={fill=white,inner sep=2pt}]
\draw (0,-4)--(0,4) node[above] {$Im$} (-4,0)--(4,0) node[right] {$Re$};
\draw[dashed] (0,0) circle (3) circle (2);
\coordinate (a) at (80:3);
\coordinate (b) at (3,0);
\coordinate (m) at (80/3:2);
\coordinate (n) at ({80/3-120}:2);
\coordinate (p) at ({80/3+120}:2);
\coordinate (o) at (0,0);
\draw (a) node[above right] {$z=|z|e^{i\theta}$};
\draw (b) node[below right] {$|z|$};
\draw (2,0) node[below left=0cm and -2em] {$|z|^{1/3}$};
\draw (m) node[right] {$|z|^{1/3}e^{i\theta/3}$};
\draw (n) node[below] {$|z|^{1/3}e^{i(\theta+4\pi)/3}$};
\draw (p) node[above] {$|z|^{1/3}e^{i(\theta+2\pi)/3}$};
\draw (.1,1.5)--(0,1.5) node[left] {$i$};
\draw (1.5,.1)--(1.5,0) node[below] {$1$};
\draw (0,0)--(a) (0,0)--(m) (0,0)--(n) (0,0)--(p);
\draw[dashed] (m)--(n)--(p)--cycle;
\end{scope}
\draw (45:0.8) node[above right] {$\theta$};
\fill[black] (a) circle (2pt) (b) circle (2pt) (m) circle (2pt) (n) circle (2pt) (p) circle (2pt) (2,0) circle (2pt);
\end{tikzpicture}
\end{center}

\vskip 2cm
\vfill
{\sc 2019.1}
\end{center}
\end{titlepage}%

\end{document}


• thank you very much!! worked here – Matheus Guimaraes Mar 16 at 16:15
• Is it possible to use the image as a cover? I am making a cover for handout of complex variables but it is not working because I am using \ documentclass [a4paper, 12pt] {article}% how to make the necessary change for compilation to take place right? – Matheus Guimaraes Mar 16 at 16:17
• @MatheusGuimaraes Change \documentclass[tikz]{standalone} to \documentclass{article} \usepackage{tikz}. – user156344 Mar 16 at 16:19
• I did this but when I compile it gives an error in '' \ pic ''. How do I correct it? – Matheus Guimaraes Mar 16 at 16:23
• @MatheusGuimaraes Make sure you have \usetikzlibrary{quotes,angles} in your preamble. – user156344 Mar 16 at 16:26