Possible to use$ \C$ for complex numbers with T2A encoding?

Question

In using pdflatex on a document in English that will include some Cyrillic text. For math, I'd like to use $\C$ for the set of complex numbers. But the T2A encoding needed for babel with its russian option gives error:

Command \C already defined.

Here's the source:

\documentclass{article}

\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
%\usepackage[main=english,russian]{babel}

\usepackage{amssymb}
\newcommand{\C}{\mathbb{C}}

\begin{document}

%{\Russian Алекс\'{а}ндров}, {\Russian Т\'{и}хонов}, and {\Russian Урыс\'{o}н}.

$\C$ denotes the set of all complex numbers.

\end{document}

The workaround

\renewcommand{\C}{\mathbb{C}}

seems to work, as in the following:

\documentclass{article}

\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[main=english,russian]{babel}
\usepackage{csquotes}

\usepackage{amssymb}
\renewcommand{\C}{\mathbb{C}}

\begin{document}

{\Russian Алекс\'{а}ндров}, {\Russian Т\'{и}хонов}, and {\Russian Урыс\'{o}н}.

$\C$ denotes the set of all complex numbers.

\end{document}

Question 1: Where is \C defined in the packages loaded (I have not been able to find it so far) and what is its meaning?

If it gives some accent or some character I'll never need, then I can use the \renewcommand workaround indicated.

If not, then...

Question 2: Except for using something less terse such as $\CC$, for the complex numbers, is there some other, safer workaround?

Answer 1

The definition of \C can be found in t2aenc.def:

\DeclareTextAccent{\C}{\LastDeclaredEncoding}{19}

It denotes a double grave accent.

Some alternatives if you don't want to redefine the macro could be to define it only in math mode, or to use a Unicode character, or to choose a different one letter macro.

MWE:

\documentclass{article}

\usepackage[T1,T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[main=english,russian]{babel}

\usepackage{amssymb}

\let\oldC\C
\def\C{\textormath{\oldC}{\mathbb{C}}}

\DeclareUnicodeCharacter{2102}{\mathbb{C}}

\newcommand{\K}{\mathbb{C}}

\begin{document}
\C{и}

$\C$ denotes the set of all complex numbers.

$ℂ$ denotes the set of all complex numbers.

$\K$ denotes the set of all complex numbers.

\end{document}

Result: