Draw a diagram illustrating roots of unity in the case of C_n

rootsofunity.tex

\begin{tikzpicture}
  \coordinate (center) at (0, 0);
  \def\radius{2cm}
  \def\n{5}
  \pgfmathsetmacro\angle{360/\n}
  \pgfmathsetmacro\startangle{90}
  
  \foreach \i in {0,...,4} {
    \coordinate (point\i) at ({\startangle+\angle*\i}:\radius);
    \coordinate (label\i) at ({\startangle+\angle*\i}:\radius+0.25cm);
    \node[anchor={\startangle+\angle*\i-90}] at (label\i) {$\omega_5^{\i}$};
  }

  \draw[salmon, thick] (point0) -- (point1) -- (point2) -- (point3) -- (point4) -- cycle;
  \draw[black, thick] (center) circle (\radius);
  \draw[->] (-2.5,0) -- (2.5,0) node[right] {$\text{x}$};
  \draw[->] (0,-2.5) -- (0,2.5) node[above] {$\text{y}$};
\end{tikzpicture}