# Unknown letter ℑ used in an equation

I need to write by hand the equation from the attached snapshot but I really don't know what letter is that seen in the front of square brackets [ . Can anyone help me ?

• This is a variant of a Fraktur-typeface J, i.e. $\mathfrak{J}$ (edit: it's a J, not I), which is used for the imaginary part of the complex number, also commonly denoted $\mathrm{Im}$, and contrasted to the real part $\mathfrak{R}$ or $\mathrm{Re}$, etc. Aug 16 '14 at 10:07
• This question appears to be off-topic because it is about typesetting.
– Danu
Aug 16 '14 at 10:14
• This is question about physics (specificaly about notation used in physics), it would be good if some people would kindly allow other people to access this site and ask such a relevant question. if i were the OP and knew about this site i would consider it natural to ask such a question, someone disagrees with this? Aug 16 '14 at 10:42
• I agree that questions about notation in physics are on-topic questions about physics. Having to invent your own name or mental model for an unfamiliar symbol is an extra cognitive load that impedes physical understanding — I remember being absent the day that my freshman professor mentioned that $\varkappa$ was a kappa, and spending the next lecture(s?) feeling too stupid to ask what that x-thing was and where was the $\kappa$ that everyone talked about. Detexify looks wonderful, but even if one has heard of it (I haven't apart from ads on phys.SE, and I mostly ignore ads) it isn't foolproof.
– rob
Aug 16 '14 at 12:28
• It's on topic if the question is about the meaning of that symbol. But the question appears to be about calligraphy: "I must to write by hand the equation from the attached snapshot ..." If that's the case, that would make the question off topic. Aug 16 '14 at 14:41

This is notation for the imaginary part of a complex number. It is a fraktur letter I, and its counterpart for the real part is a fraktur letter R. Thus, if $z=x+iy$ and $x,y$ are real, one writes $$\mathfrak{R}\,z=x\ \ \text{ and }\ \ \mathfrak{I}\,z=y.$$ A good chart of the fraktur alphabet is in this Yale resource, which includes handwriting guidance, though some variation can be seen in google image searches. In LaTeX the quickest way to produce this is as the defaults of the commands \Re and \Im (though it is common for people to change this default), and which produce $\Re$ and $\Im$. Alternatively, you can use \mathfrak{R} and \mathfrak{I}, which produce $\mathfrak{R}$ and $\mathfrak{I}$; these are similar in the MathJax font displayed here but the specifics can vary on different systems.

In my experience this is an older notation which has been superseded, pretty much everywhere, by the uppercase combinations $\mathrm{Re}$ and $\mathrm{Im}$: $$\operatorname{Re}(z)=x\ \ \text{ and }\ \ \operatorname{Im}(z)=y.$$ These are typeset using \operatorname{Re} and \operatorname{Im}, although \mathrm usually works equally well. In handwritten work, most people denote the real and imaginary parts in this way; if you are making notes on a book which has the old notation, it is perfectly OK to use the new one, and it will not cause confusion for anyone reading your notes.

One thing to note is that fraktur is not a completely fixed font; it is more of a style of handwriting and there is a fair bit of variation in how each particular letter is drawn in different sources (for a sample, see the google images results for 'fraktur'). The particular $\mathfrak{I}$ in your image is relatively similar to how some fraktur fonts display the J (which sort of looks like $\mathfrak{J}$, but see the image results for the variation), but that is more of a fluke. The correct character to use is the I.

• How to write it by hand using a pen or a pencil? Aug 16 '14 at 13:51
• Well, then have a good day. Aug 16 '14 at 14:20
• I'm not the down voter, but this is not correct. While \mathfrak I, \mathfrak J and \Im appear to be very similar in mathjax (to wit: \mathfrak I: $\mathfrak I$, \mathfrak J: $\mathfrak J$, \Im: $\Im$), they are not the same using the TeXLive distribution. You don't even need the mathfrak font to use \Im. It's a part of basic LaTeX, provided by fontmath.ltx. Aug 16 '14 at 14:23
• @PratyayGhosh -- How to write it by hand? Simple: Use Im. That's a whole lot easier to write than is the fraktur character $\Im$, and Im says exactly what the intent is. Aug 16 '14 at 14:31
• @David I did find this answer with at least some logic behind it. Aug 16 '14 at 17:52

If it is actually the imaginary part of a complex variable, then just write $Im[\cdot]$ instrade of the curly character.

• I don't see how this is helpful. We now use the upright form $\operatorname{Im}$, but one cannot simply ignore a prevalent old notation simply because one doesn't like it much. -1. Aug 16 '14 at 13:00
• I never said to ignore it depending on the liking. Numlock wanted to write it by hand. What do you suggest him? Use a calligraphy pen whenever he want to write imaginary part of a complex variable. Aug 16 '14 at 13:50
• No, I suggest that the OP write $\operatorname{Im}$ in their own work, but this will not help them make sense of older texts that do use the $\Im$ notation, which is the question at hand. Unless, of course, you're suggesting that the OP scratch out all occurrences of $\Im$ and scribble $\operatorname{Im}$ on top, or that all old books be reprinted and replaced, with the new notation in place. Aug 16 '14 at 14:13
• read the first line. Aug 16 '14 at 14:19