# How should imaginary numbers be typeset?

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).

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Somebody prescribes it has to be upright (because it's a constant; I don't agree by any means). You can try \newcommand{\di}{{i\mkern1mu}} to give some room. –  egreg Dec 8 '12 at 16:48
If you want to quit the dot of the i you can use \imath, to get more freedom. –  Manuel Dec 8 '12 at 16:50
@egreg. That does the trick. Thanks. But why the surroudning parentheses? –  A.Ellett Dec 8 '12 at 16:55
@A.Ellett The exponent is to the whole subformula {i\mkern1mu}; otherwise i\mkern1mu^2 would have the exponent to an empty subformula. –  egreg Dec 8 '12 at 17:03
Unrelated suggestion: define \def\I{i} and simply use \I everywhere in your math. You can fix your one macro later, after finishing your manuscript. After many similar problems, I found this helps me maintain productivity. –  Alex Nelson Dec 8 '12 at 20:33

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.

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Personally I do not see any visual clash. –  Yiannis Lazarides Dec 11 '12 at 8:00
@YiannisLazarides Neither do I, but it's a personal opinion and is as respectable as A.Ellett's. :) –  egreg Dec 11 '12 at 8:04

I'd always use a math italic i. But conventions vary Many engineering disciplines use j rather than i. Unicode has a specific slot U+2148 (ⅈ) which is a double struck italic i. This is the &ImaginaryI; (ⅈ) entity in MathML and HTML5. (The convention started with Mathematica, I can't say I like it much, but it's there if you want an unambiguous notation.)

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If you're looking for conventions then Elsevier, (a huge publisher) has guidelines: "Preparing Articles in LaTeX", which state (page 11 of PDF, 10 of guidelines) when i is used as an imaginary it is conventionally typeset in a Roman typeface. The example they give has the dot on the i, Roman typeface makes the i upright.

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But they have different instructions for different journals. –  Andrew Swann Dec 9 '12 at 10:21
"Elsevier publishes 250,000 articles a year in 2,000 journals" and "In 2003 its publishing accounted for 25% of the world market in science, technology, and medical publishing". That's a huge influence.See here too. –  DJP Dec 9 '12 at 16:15
I am not disputing that. But different subject areas, have different conventions and Elsevier follows that to some extent. E.g. the journal Differential Geometry and its Applications does not force upright i's on authors as that is not the convention in pure mathematics (see e.g. vol 26(5) page 563 near the top). –  Andrew Swann Dec 9 '12 at 18:00

Der Brockhaus Naturwissenschaft und Technik Band 2 (2003) (famous german Encyclopedia on Science) uses upright i

Bergmann Scheafer Lehrbuch der Experimantalphysik (2010) (very famous and rich books on physiks) uses upright i (as fa as i remember)

One possible explanation is, that i is not a variable which usually are typeset in italic. According to a DIN (german industry standard) j for imaginary numbers is allowed in electronic engineering.

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Math papers usually have an italic "i"; however in applied mathematics it is common to find the upright "i", which is also prescribed in ISO norms. Mathematicians have used the italic "i" for a more than a couple of centuries, and ISO norms won't bother them. ;-) –  egreg Dec 8 '12 at 20:25
Well the thing is here, i think, that a author should ask himself whether his readers can or should understand what is meant even when it's not written down somewhere. Anyhow the i looks like, mixing imaginary i and variable i without difference in formatting would lead to a very poor result. –  bloodworks Dec 8 '12 at 20:52

it's the dot on the $i$ my eye is visually objecting to ...

you could use what I have been using which is a dotless i:

## Code:

\documentclass{article}
\newcommand*{\I}{\imath}%
\begin{document}
$\I^2=-1$
\end{document}

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To paraphrase Paul J. Nahin who wrote a book on the history of i, it would be no small job to do it well from the Hindus downwards. Here is an Engineers perspective.

In Engineering we have used an i (in all topics, such as thermodynamics, mechanics etc) with the exception of Electrical Engineering, where we use a j and for a good reason as the i is normally used to denote the current. A math italic is the best notation and clear across all disciplines.

As a matter of good practice, use what is most common in your field. If you worried about confusion and want to take the dot out of the i, please don't, as anyone that is confused with such a simple matter is unlikely to spot that the "i" is a dotless "i", not to mention the confusion of Turkish mathematicians. David's suggestion of U+2148 (ⅈ), just looks ugly.

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