[Tex/LaTex] How should imaginary numbers be typeset

best practicesspacingsuperscripts

I've never had to typeset complex numbers before and I'm finding that I'm uncertain about what best-practices are. My question is really about typesetting just i. (Hence my title referring to imaginary as opposed to complex numbers.)

I would like to be consistent with the textbook which uses a slantstyle. But aside from the choices of the textbook, I'm curious about what others think: Should it be upright? Should it be italic like a variable name?

When I use the default math style, I don't like the appearance, particularly in conjunction with exponents. It looks too crowded and busy to me. Is this just because I'm not used to typesetting for complex numbers? Or, is there some kind of italic correction I could do that would fix things: \/ seems to be ignored in math mode.

Here's my minimal working example:

\documentclass{article}
\usepackage{amsmath}
\pagestyle{empty}
\usepackage[margin=2.25in]{geometry}
\setlength{\parindent}{0pt}
%%
\newcommand{\mi}{\mathrm{i}} %% roman "i"
\newcommand{\di}{i}          %% default math "i"
\begin{document}

    \verb=\mathrm= style: (not consistent with font choice of textbook)
        \begin{align*}
        \mi^0 &= 1     \\
        \mi^1 &= \mi   \\
        \mi^2 &= -1    \\        
        \mi^3 &= -\mi 
        \end{align*}

    Default math style: (better matches the style of the textbook, but already looking crowded.)
        \renewcommand{\di}{i}
        \begin{align*}
        \di^0 &= 1     \\
        \di^1 &= \di   \\
        \di^2 &= -1    \\        
        \di^3 &= -\di 
        \end{align*}
    Whichever choice, the following looks too busy. 
    \begin{align*}
        \mi^n &= \mi^{4\times k + r} = \mi^{4\times k} \times \mi^4 = (\mi^4)^k \times \mi^r = 1^k \mi^r = \mi^r \\
        \di^n &= \di^{4\times k + r} = \di^{4\times k} \times \di^4 = (\di^4)^k \times \di^r = 1^k \di^r = \di^r
    \end{align*}
    And if I change the \verb=\times= to \verb=\cdot= it looks even worse:
    \[
        \di^n = \di^{4\cdot k + r} = \di^{4\cdot k} \cdot \di^4 = (\di^4)^k \cdot \di^r = 1^k \di^r = \di^r
    \]

\end{document}

I know I could completely drop using \times or \cdot but for my particular audience I want to emphasize the multiplication.

I think it's the dot on the $i$ my eye is visually objecting to (in which case there's not much to do about it, I guess).

enter image description here

Best Answer

The possible visual clash of the dot with the exponent can be cured by adding a small kern:

\newcommand{\iu}{{i\mkern1mu}}

Experiment also with smaller kerns and note that the setting depends on the font used, so it can't be a universal recipe. Here's an example: left the kerned version, right the unkerned one.

enter image description here

Some people maintain that mathematicians should conform to ISO standards (see Timtro's answer), but my opinion is that ISO standards should conform to centuries long tradition of mathematical typesetting in the first place. We can look at an article by Sophie Kowalewski published by the Acta Matemathica, one of the journals that set the highest standards for math typesetting. On the first page we see

enter image description here

and on page 89

enter image description here

There is no doubt whatsoever for the meaning of “i” and “d”.

Maybe this is considered too old fashioned. Here is an example from a big publisher, with considerably high standards. It's an excerpt from a paper in “Differential Geometry and its Applications”, volume 26(5) 2008, pages 553–565 (top of page 563). Access is restricted, so I provide a cropped image showing just the important graphic part and no complete text.

enter image description here

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