Make paired delimiter with prefix for Re and Im

Question

I'm trying to make a new command for something like this:

\operatorname{Re}\left\lbrace\num{1+2i}\right\rbrace

Because I'm using the mathtools package already I tried to do something like this: (And I have to undefine the previous \Re and \Im commands, because they are ugly and this command should be obviously called \Re and \Im.)

\let\Re\undefined
\let\Im\undefined
\DeclarePairedDelimiter\Re{\operatorname{Re}\lbrace}{\rbrace}
\DeclarePairedDelimiter\Im{\operatorname{Im}\lbrace}{\rbrace}

This will work, but will also spit put many errors. Like: Missing { inserted. \end{align} and so on.

Then I thought: Yes, this is probably, because the font can not scale (and shouldn't), like the \lbrace and \rbrace. And I tried something like this:

\let\Re\undefined
\let\Im\undefined
\DeclarePairedDelimiter\braces{\lbrace}{\rbrace}
\newcommand{\Re}{1}{\operatorname{Re}\braces*{#1}}
\newcommand{\Im}{1}{\operatorname{Im}\braces*{#1}}

But this will produce:

Missing $ inserted. \newcommand{\Re}{1}{\operatorname{Re}

Missing \begin{document}. \newcommand{\Re}{1}{\operatorname{Re}

Inserting \ensuremath or something like that doesn't help much.

Last try:

\let\Re\undefined
\let\Im\undefined
\newcommand{\Re}{1}{\operatorname{Re}\left\lbrace #1 \right\rbrace}
\newcommand{\Im}{1}{\operatorname{Im}\left\lbrace #1 \right\rbrace}

Missing $ inserted. \newcommand{\Re}{1}{\operatorname{Re}

Missing \begin{document}. \newcommand{\Re}{1}{\operatorname{Re}

You can't use `macro parameter character #' in math mode. ...nd{\Re}{1}{\operatorname{Re}\left\lbrace #

It can't be this hard to make something like this work, or can it? I really don't know what I should try next, or what am I even doing wrong.

Answer 1

You have the incorrect syntax for \newcommand.

\newcommand{\Re}{1}

should be

\newcommand{\Re}[1]

Answer 2

You can use the \DeclarePairedDelimiterXPPfrom mathtools. It will define \Reand \Im commands, which have a star version (adds a pair of implicit \left \right in front of the delimiters), but they also accept an optional argument among \big, \Big, \bigg and \Bigg, which adds a pair oof implicit \bigl \bigr, &c.

\documentclass[10pt]{article}
\usepackage{mathtools} %
\let\Re\undefined
\let\Im\undefined
 \DeclarePairedDelimiterXPP\Re[1]{\operatorname{Re}}{\lbrace}{\rbrace}{}{#1}
 \DeclarePairedDelimiterXPP\Im[1]{\operatorname{Im}}{\lbrace}{\rbrace}{}{#1}

\begin{document}

   \[ \Re*{\frac{z-1}{z + 1}}\qquad \Im[\Big]{\frac{z-1}{z + 1}} \]%

\end{document}