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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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SarthakC
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    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. – njuffa Dec 04 '16 at 08:30
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    Was it $\iota$ (\iota) or $\imath$ (\imath)? ;) LaTeX, at the very least, clearly recognizes the latter as an alternative to $i$ :) – Danu Dec 04 '16 at 10:33
  • @njuffa - see this post for scan of the non-use by Euler of $i$ for $\sqrt -1$... – Mauro ALLEGRANZA Dec 04 '16 at 10:54
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    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". – Mauro ALLEGRANZA Dec 04 '16 at 11:05
  • @MauroALLEGRANZA Thank you very much for the link to the scan in your second comment which clearly shows the use of $i$. I am puzzled by your reference to "non-use" in your first comment. Is that indicating disagreement with my statement about Introductio in Analysis Infinitorum? I was referring to e.g. Lib. 1, p. 98 – njuffa Dec 04 '16 at 16:35
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    @njuffa - the linked post shows that Euler in his Introductio used $i$ but not to denote $\sqrt -1$... – Mauro ALLEGRANZA Dec 04 '16 at 16:46
  • @Danu: I was not aware of \imath! Thanks for that. So if not \iota at least I know that an "i without the tittle" is valid notation... – SarthakC Dec 04 '16 at 22:36
  • @njuffa: So I guess Euler used $i$ then. Who did start using $\iota$ (\iota) or $\imath$ (\imath) then? – SarthakC Dec 04 '16 at 22:41
  • In TeX, we use \imath for an i where we will put something above it, for example $\hat{\imath}; \check\imath; \overline\imath$ ... but we don't use \imath by itself. – Gerald Edgar Dec 05 '16 at 14:24

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For an early occurrence of "iota", see :

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

Mauro ALLEGRANZA
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  • 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. – SarthakC Dec 05 '16 at 17:42