LaTeX Forum

\documentclass[11pt]{scrartcl}

\usepackage{amsmath}
\usepackage{amssymb}

\newcommand{\menge}[2]{\left\{ #1 ~\middle\vert~ #2 \right\}}
\newcommand{\mengeB}[2]{\left\{ #1 \bigm\vert #2 \right\}}

\begin{document}
	~\\using middle:
	\[ S^3 = \menge{(z,w)\in \mathbb{C}^2}{\frac{|z|^2}{|w|^2} = 2} \]
	\[ \menge{(z,w)}{|z|=|w|=1} .\]
	using big:
	\[ S^3 = \mengeB{(z,w)\in \mathbb{C}^2}{\frac{|z|^2}{|w|^2} = 2} \]
	\[ \mengeB{(z,w)}{|z|=|w|=1} .\]
\end{document}

\documentclass{scrartcl}
\usepackage{amsmath}
\usepackage{amssymb}
\newcommand{\menge}[2]{\left\{\strut #1 ~\middle\vert~ #2 \right\}} %https://tex.stackexchange.com/a/364282

\begin{document}
   \[ S^3 = \menge{(z,w)\in \mathbb{C}^2}{\frac{|z|^2}{|w|^2} = 2} \]
   \[ \menge{(z,w)}{|z|=|w|=1} .\]
\end{document}

\documentclass{scrartcl}
\usepackage{amsmath}
\usepackage{amssymb}
\newcommand{\menge}[3][]{%
  \IfArgIsEmpty{#1}{%
    \ensuremath{\left\{\strut #2 ~\middle\vert~ #3 \right\}}%
  }{%
    \ensuremath{#1\{#2 ~#1\vert~ #3 #1\}}%
  }%
}

\begin{document}
   \[ S^3 = \menge{(z,w)\in \mathbb{C}^2}{\frac{|z|^2}{|w|^2} = 2} \]
   \[ \menge{(z,w)}{|z|=|w|=1} .\]
   \[ S^3 = \menge[\Bigg]{(z,w)\in \mathbb{C}^2}{\frac{|z|^2}{|w|^2} = 2} \]
   \[ \menge[\big]{(z,w)}{|z|=|w|=1} .\]
\end{document}