[Tex/LaTex] Euler and minus sign

Question

I'm trying to define a macro to typeset Eulers complex e-power with or without a minus sign in its argument. I would like the macro to automatically detect if its argument starts with a -. I have the following MWE which uses and optional argument:

\documentclass[a4paper,12pt,fleqn]{article}

\def\imaginaryunit{j}                  % the imaginary unit, i for mathematician and theoretical physicist, j for the rest of the world.
\def\imunit{\mathrm{\imaginaryunit}}   % ... in upright math
\def\ce{\mathrm{e}}                    % the constant e, upright of course
\makeatletter
\def\epowim{\@ifnextchar[{\epowimi}{\epowimi[]}}       % e to-the-power-of imaginary unit
\def\epowimi[#1]#2{\ce^{#1\if\imaginaryunit j\relax\,\fi\imunit#2}}       % e to-the-power-of imaginary unit
\makeatother

\begin{document}

\begin{equation}
\epowim{\alpha}\qquad \epowim[-]{\alpha} \qquad \ce^{-\imunit\alpha}
\end{equation}

\end{document}

So I would like a macro that detects if its argument starts with a -:

\epowim{-\alpha}

should detect the - and place it before the imaginary unit instead of placing it after the imaginary unit.

So the question is if it can be done and how.

Answer 1

Something like this?

\documentclass[a4paper,12pt,fleqn]{article}
\def\imaginaryunit{j}                  % the imaginary unit, i for mathematician and theoretical physicist, j for the rest of the world.
\def\imunit{\mathrm{\imaginaryunit}}   % ... in upright math
\def\ce{\mathrm{e}}                    % the constant e, upright of course
\newcommand\epowim[1]{\ce^{\epowimaux#1\relax\endep}}
\def\epowimaux#1#2\endep{\ifx-#1\relax-\imunit\else%
  \if j\imaginaryunit\relax\,\fi\imunit#1\fi#2}
\begin{document}
\[
\epowim{\alpha}\qquad \epowim{-\alpha} \qquad \ce^{-\imunit\alpha}
\]
\[
\epowim{x+t}\quad\epowim{-x+t}\quad\epowim{-}\quad\epowim{}
\]
\def\imaginaryunit{i}
\[
\epowim{\alpha}\qquad \epowim{-\alpha} \qquad \ce^{-\imunit\alpha}
\]
\[
\epowim{x+t}\quad\epowim{-x+t}\quad\epowim{-}\quad\epowim{}
\]
\end{document}