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In electronics, $j$ is used for a square root of $-1$, because $I$ is current. Who introduced this and when? And was it really necessary, given that (at least now) current's symbol is capitalised? Perhaps it wasn't at the time, but as best I can tell Ampère didn't use lower case.

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  • $\begingroup$ Current in electronics certainly is represented by a small italic i today, particularly for small signal analysis, where complex arithmetic is used extensively! But as for when that started, I couldnt tell you. $\endgroup$ – Sam Gallagher May 27 at 12:20
  • $\begingroup$ @SamGallagher I was only ever taught to use $I$, but I can understand why a field called "small signal analysis" would use $i$, because it's probably focused on perturbations to background electromagnetism. $\endgroup$ – J.G. May 27 at 12:51
  • $\begingroup$ Its a simplified model for circuit analysis, where changes are assumed very small in active (e.g. transistor, op amp, etc) circuits. All "small signal" voltages and currents are represented by lower-case v and i. $\endgroup$ – Sam Gallagher May 28 at 13:11
  • $\begingroup$ Note that i refers to $\sqrt{-1}$ while i is often the unit vector in the x-axis. $\endgroup$ – Carl Witthoft May 28 at 13:30
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    $\begingroup$ @CarlWitthoft: The unit vector would normally be $\hat{\textbf{i}}$, not just $i$. $\endgroup$ – Ben Crowell May 30 at 0:17
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The symbol i is still used in mathematics; j is an invention of an electrical engineers, usually attributed to Charles P. Steinmetz. See for example Introduction of $\imath$ and $\jmath$ notations for the imaginary unit

As to why j was chosen, the following is quoted from a 1921 book, "Tables of Complex Hyperbolic and Circular Functions" by Arthur Edwin Kennelly. I am sure older ones will also explain the same.

Book image

My feeling is that since j was chosen by a German-born American (Steinmetz), it may be possible to attribute the similarity of i and j in German e.g. Iodine (symbol I) is Jod (symbol J) in German. However the letter i was also introduced by Gauss, who happened to be German, but at that time, Latin was the language of science. This is just my pure speculation.

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