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.)
\iota
) or $\imath$ (\imath
)? ;) LaTeX, at the very least, clearly recognizes the latter as an alternative to $i$ :) $\endgroup$