# How can I write a complex exponential in LaTeX so that it looks presentable?

I have the complex exponential written as:

$$e^{i \frac{2\pi}{5}}$$


which appears as:

I have the complex exponential written as:

$$e^{-i \dfrac{2\pi}{5}}$$


which appears as:

Is there a 'better' way to represent this so it looks presentable?

• Try using / instead of \frac in the exponent. Commented Mar 7 at 0:31
• certainly dont use dfrac that is forcing displaystyle in the superscript Commented Mar 7 at 1:13
• Do you really need a fraction? Would e^{-i 0.4\pi} suffice? Commented Mar 7 at 14:12
• I disagree with the premise that there's anything wrong with e^(i\frac{2\pi}5}. Looks perfectly presentable. Commented Mar 7 at 15:51

Is there a 'better' way to represent this?

Use inline-math fraction or "slash" notation: e^{-i 2\pi/5}. Depending on the field you're in, it may be customary to place the 2\pi factor ahead of i. Do also consider using \exp(...) notation instead of e^{...} notation.

\documentclass{article}
\begin{document}
$e^{-i 2\pi/5} \quad e^{-2\pi i/5} \qquad \exp(-i 2\pi/5) \quad \exp(-2\pi i/5)$
\end{document}

• Also depends if you want to comply with ISO or not. Commented Mar 7 at 4:19
• According to ISO standard "e" is a constant and it should be upright. Widely not followed though by the majority of authors. See tug.org/TUGboat/Articles/tb29-2/tb92guiggiani.pdf Commented Mar 7 at 6:13
• @yannisl - Thanks. Incidentally, it's not only "e" but "i" too that is supposed to be rendered in an upright/roman font shape; after all, "i" is a constant... Some zealots even claim that the symbol for \pi should be rendered using an upright variant of the glyph, since \pi is also a constant. As you take care to point out, though, this particular norm is widely ignored. Back to the query at hand: I'll admit that I didn't think about this particular norm when I posted my answer, possibly because I was focused on the "presentability" criterion mentioned in the title of the OP's query.
– Mico
Commented Mar 7 at 6:24
• @yannisl I pulled several books off of my bookshelf, and not a single one uses an upright e or i in such instances (and I personally think such constructs look quite ridiculous). I will also point out that using an upright "d" in integrals is inconsistent with how such things are used in mathematics: the quantity is not "d" followed by "x"; it is "dx" (i.e., a variable like x that is infinitesimally small). Point is: use an upright e, d, and i if you want, but you would probably be in the minority by doing so. Commented Mar 8 at 2:57
• @karlh Agreed, I do the same, one is not bound to use the ISO Standard, although I understand the rationale behind the suggestion for upright. When in doubt do what Knuth would do!. But if you had exp raised to {abcde}, where abcde are variables... you get my drift... tex.stackexchange.com/questions/14821/… there are many discussions about this. I did mentioned it for completeness. Commented Mar 8 at 4:19

My suggestions would be any of the following:

$e^{-2\pi i/5} \qquad \exp\left(\frac{-2\pi i}{5}\right) \qquad \exp\left(-\frac{2}{5}\pi i\right)$


Other variants are also possible/common. These display as in the attached image.

• 2/5 is such a narrow fraction that it won't be a problem, but with wide fractions a negation in front at the same level as the fraction bar can sometimes look like it's part of the fraction bar--especially if the printing/copying is of low quality. I usually look for ways to avoid it (such as your first two options). Commented Mar 7 at 0:56
• Given that 2/5 is a simple fraction I'd use \tfrac in the lat example. I might even scale the ()'s manually (\bigl ... \bigr) to avoid the space after \exp Commented Mar 7 at 8:35
• Look at the huge gap between exp and the opening parenthesis: this is a perfect example of why \left and \right shouldn't be used unless really necessary ;-) Commented Mar 7 at 9:26
• @campa I actually prefer the extra space most of the time. In this case, it could almost go either way, but there are plenty of times that I have to manually add space before a parenthesis if it's created by \bigl and friends. Using braces around the argument sometimes helps, too. Commented Mar 8 at 2:52

I do not see ugly \frac nor /, but ... Maybe \nicefrac?

\documentclass[twocolumn]{article}
\usepackage{tabto,parskip}
\usepackage{units}
\begin{document}
\verb!\frac!\tab $$e^{-i\frac{2\pi}{5}}$$\par
\verb!\slash !\tab  $$e^{-i2\pi\slash 5}$$\par
\verb!\nicefrac!\tab $$e^{\nicefrac{-i2\pi}{5}}$$\par
\verb!\nicefrac!\tab $$e^{-i(\nicefrac{2\pi}{5})}$$\par
\verb!\slash !\tab  $$e^{-i(2\pi\slash 5)}$$\par
\end{document}


$e^{i\alpha}$ with angle $\alpha=2\pi/5$ maybe a nicer approach, especially if you have some other values of your angle $\alpha$ in the paper, since it emphasizes the meaning of $\alpha$ as an angle, which is intuitive for the reader.