I'm interested in particular in knowing about when $\iota$ began to be used as the imaginary unit/who began to use it.

A majority of all text books that I have seen tend to just use $i$ as the imaginary unit. However, I remember being taught back in high school (in India) that the standard usage for the imaginary unit was $\iota$, which is most often just replaced with i everywhere. I can't find any source to back this up though --- for example wiki just says that $\iota$ is used when $i$ is being used for something else.

Am I remembering incorrectly? Was iota used initially historically maybe? Or is using iota just some notation that someone else tried to introduce? It definitely was/is considered valid notation if people are doubting the premise of the question (for example a quick search "imaginary unit iota" on Google comes up with several people using this notation. Even for example in the text that OP mentions here also talks about $\iota$ as valid notation.)

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    $\begingroup$ In Introductio in Analysis Infinitorum (1748) Euler still writes $\sqrt{-1}$, and according to this answer he only later introduced the letter $i$ for the imaginary unit. I have not been able to find a scan of the document that shows Euler's first use of $i$. I have never encountered the use of $\iota$ instead of $i$, but am aware that $j$ is used instead in electrical engineering. $\endgroup$
    – njuffa
    Dec 4, 2016 at 8:30
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    $\begingroup$ Was it $\iota$ (\iota) or $\imath$ (\imath)? ;) LaTeX, at the very least, clearly recognizes the latter as an alternative to $i$ :) $\endgroup$
    – Danu
    Dec 4, 2016 at 10:33
  • $\begingroup$ @njuffa - see this post for scan of the non-use by Euler of $i$ for $\sqrt -1$... $\endgroup$ Dec 4, 2016 at 10:54
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    $\begingroup$ For the first printed occurrence in Euler (1794, reprint of 1777 Euler's paper "De Formulis Differentialibus Angularibus maxime irrationalibus quas tamen per logarithmos et arcus circulares integrare licet," addressed to the 'Academiae') published posthumously in his Institutionum calculi integralis, 2nd ed, vol.4, pp.183-194 : "formulam $\sqrt -1$ litera $i$ in posterum designabo". $\endgroup$ Dec 4, 2016 at 11:05
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    $\begingroup$ @njuffa - the linked post shows that Euler in his Introductio used $i$ but not to denote $\sqrt -1$... $\endgroup$ Dec 4, 2016 at 16:46

1 Answer 1


For an early occurrence of "iota", see :

§10. writing $\iota$ for $\sqrt {-1}$, [...].

  • $\begingroup$ Oh, this is almost exactly like the kind of thing I was looking for. If no-one else answers soon with maybe a discussion of an earlier source/if this is one of the earliest source using this, then I'll accept this answer. $\endgroup$
    – SarthakC
    Dec 5, 2016 at 17:42

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