[Tex/LaTex] Picture indicating the fifth roots of unity

Question

I would like to have the unit circle, centered at the origin, on the Cartesian plane drawn. The origin is to be marked with a dot and labeled "O" and five dots are to be drawn on the circle, one on the x-axis, and the others at k(2\pi/5) radians from the positive x-axis for each integer 1 \leq k < 5, and they are to be labeled "w_{k}". Arrows are to be drawn from the origin to each w_{k}, too. One angle is to be drawn and labeled – the one from the positive x-axis to the ray through w_{1}.

I have included some of the code. It starts with the following commands.

\tikzset{mydot/.style={fill,circle,inner sep=1.5pt}}

Is there a manual that explains each of these commands? I guess that this is instructing LaTeX how to make the dots indicating the coordinates each time "\mydot" is in the code.

\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{newlfont}
\usepackage{mathtools}
\usepackage{tikz}

\tikzset{
mydot/.style={
  fill,
  circle,
  inner sep=1.5pt
  }
}

\begin{document}

\begin{tikzpicture}[>=latex]


% the coordinates of the vertices
\coordinate (O) at (0,0);
\coordinate (w_{1}) at (\cos(2\pi/5), \sin(2\pi/5));

% the axes
\draw[help lines,->] (-1.5,0) -- (1.5,0);
\draw[help lines,->] (0,-1.5) -- (0,1.5);

% labelling the vertices
\node[mydot,label={below:$O$}] at (O) {};
\node[mydot,label={right:$w_{1} = \bigl(\cos(2\pi/5), \sin(2\pi/5)\bigr)$}] at (w_{1}) {};


% the arcs for the angle
\begin{scope}[gray]
\draw[->]
  (1,0) +(0:0.5cm) arc [radius=1cm,start angle=0,end angle=2\pi/5] node[midway,right] {$2\pi/5$};
\end{scope}

\end{tikzpicture}
\end{document}

Answer 1

To learn more about TikZ read pgfmanual.pdf. Via the macro \n you can adjust the order of the root to be taken.

\documentclass[tikz]{standalone}
\usepackage{amsmath}% for \Re and \Im
\def\n{5}
\begin{document}
\begin{tikzpicture}[
  dot/.style={draw,fill,circle,inner sep=1pt}
  ]
  \draw[->] (-2,0) -- (2,0) node[below] {$\Re$};
  \draw[->] (0,-2) -- (0,2) node[left] {$\Im$};
  \draw[help lines] (0,0) circle (1);

  \node[dot,label={below right:$O$}] (O) at (0,0) {};
  \foreach \i in {1,...,\n} {
    \node[dot,label={\i*360/\n-(\i==\n)*45:$w_{\i}$}] (w\i) at (\i*360/\n:1) {};
    \draw[->] (O) -- (w\i);
  }
  \draw[->] (0:.3) arc (0:360/\n:.3);
  \node at (360/\n/2:.5) {$\alpha$};
\end{tikzpicture}
\end{document}

For 1 < n < 13: