This is a simple question.

I know of two different notational conventions for the complex conjugate of a complex number. Perhaps there are more than two.

Which notation should I use in questions or answers in the Mathematics Stack Exchange?


$$ z \ \triangleq \ x \ + \ i\,y \qquad \qquad x,y \in \mathbb{R} $$


$$ \overline{z} \ = \ x \ - \ i\,y $$


$$ z^* = \ x \ - \ i\,y $$

Which convention should I use? Or is there a third convention (that I don't know about) that is even more conventional?

  • 3
    $\begingroup$ This is probably better suited to the Math Stack Exchange site. That said, I think $\overline z$ is more commonly used. $\endgroup$
    – lulu
    Apr 6, 2022 at 22:16
  • $\begingroup$ I thought it was kinda a meta-math question, @lulu . It's not so much about the content of mathematics, but more of a math style question. $\endgroup$ Apr 6, 2022 at 22:22
  • $\begingroup$ My plan is to bring to the math SE some nagging electrical engineering signal processing questions. That's mostly what I do here anyway. (Oh, I guess I asked one question about combinatorics with application to voting systems.) $\endgroup$ Apr 6, 2022 at 22:24
  • 2
    $\begingroup$ I'm not fussed about complex conjugates, but what is that triangle over the equals sign supposed to do? $\endgroup$ Apr 7, 2022 at 0:02
  • $\begingroup$ I have actually encountered $z^*$ for complex conjugate more often than $\bar z$. In fact, I have seen $\bar z$ with many different meanings, but never $z^*$ for something other than a complex conjugate. My background is engineering and physics though, not mathematics. $\endgroup$
    – user400188
    Apr 7, 2022 at 0:02
  • 7
    $\begingroup$ Generally speaking, as it seems you are aware the notation is not universal, just pick the one you are most comfortable with, specify explicitly , clearly, and early in your post what you mean, and then go ahead and use that. Keep in mi d the responses may use whatever notation they prefer, though. $\endgroup$ Apr 7, 2022 at 0:41
  • 4
    $\begingroup$ @GerryMyerson: I believe it is extremely annoying notation some people use to denote a definitional equal sign (like $:=$ is sometimes used, especially in older computer languages). $\endgroup$ Apr 7, 2022 at 0:43
  • 2
    $\begingroup$ Once you've identified $z\in \mathbb C$, either notation will be fine. $\endgroup$
    – hardmath
    Apr 7, 2022 at 1:09
  • 1
    $\begingroup$ This really is a question about mathematical notation, rather than a question about the notation which should be used on Math SE. Even on Math SE, the convention will vary based on context (if you are only working in $\mathbb{C}$, then $\overline{z}$ is likely the best option, but in more general spaces, e.g. $C^\ast$ algebras over $\mathbb{C}$, $z^\ast$ might be better. $\endgroup$
    – Xander Henderson Mod
    Apr 7, 2022 at 1:49
  • 1
    $\begingroup$ Yes @ArturoMagidin is correct. It means "equal by definition" and it's used quite a bit in electrical engineering texts. It's meant to save us from the argument: "Where did you get the equation $N = 2^p$ from? You haven't shown it to be true." Like "I made it up." Sorry to annoy you and Gerry. I have seen this notation: "$\equiv$" used in math textbooks. But it has a different meaning. $\endgroup$ Apr 7, 2022 at 3:39
  • 3
    $\begingroup$ And, BTW, I consider this a meta question, not worthy of wasting space in the main site. I cannot imagine why you guys don't think it is. $\endgroup$ Apr 7, 2022 at 3:45
  • 2
    $\begingroup$ It might be a meta question but it would get many more views and answers/replies/comments on the main site. People come to Meta when they're interested in how the main site runs, mostly, so you're denying yourself a valuable audience by choosing to post here. $\endgroup$
    – postmortes
    Apr 7, 2022 at 5:49
  • 2
    $\begingroup$ On this site I would expect most users to be familiar with both notations. At least those who count. Also, there is no way we could enforce only one to be used. Even if we wanted to. Of course, you can clarify the meaning when posting. Last but not least, props for asking! $\endgroup$ Apr 7, 2022 at 8:14
  • 4
    $\begingroup$ @JyrkiLahtonen "At least those who count"? Doesn't it sound a little contemptuous? $\endgroup$ Apr 7, 2022 at 16:34
  • 1
    $\begingroup$ My advice. Use $\overline{z}$ on a mathematics forum and use $z^*$ on a physics forum. (If you never see the asterisk used for anything other than complex conjugate, then you do not do much mathematics.) $\endgroup$
    – GEdgar
    Apr 8, 2022 at 11:47


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