\documentclass[10pt]{book}
\usepackage{amsmath}  % removing this bypasses the problem
\begin{document}
\begin{equation} % Using \[ instead is ok
y(n) = \langle x\rangle. % \qquad\hbox{($x$ real)}
\label{eq1}
\end{equation} % Using \] instead is ok
\begin{equation} % Using \[ instead is ok
y_2(n) 
\label{eq2}
= \langle x_2\rangle. % \qquad\hbox{($x$ real)}
\end{equation} % Using \] instead is ok
See eq.~\ref{eq1} and eq.~\ref{eq2}.
\end{document}
