Talk:Imaginary number

This article was originally a redirecty to complex number, but has been replaced by a brief explanation of the terminology and a link to that article to avoid confusion. Greg Woodhouse 10:34, 16 April 2007 (CDT)

Confusing sentence

I don't understand the sentence

Sometimes such complex numbers are called "pure imaginary numbers" to distinguish them from other complex numbers that are not real.

It's not very clear what the antecedent of "such complex numbers" is; I assumed it is "a complex number whose real part is zero" and fixed the sequence accordingly. More importantly, the way I read the sentence, it says that such complex numbers are called "pure imaginary numbers" because in that way, they are are distinguished from other complex numbers. But that seems a rather odd reason; you could just as well call them simply "imaginary numbers". -- Jitse Niesen 07:59, 17 April 2007 (CDT)

It's just a matter of mathematical practice (at least among algebraists). Numbers of the form $bi$ where $b\in \mathbb {R} \scriptstyle$ are called pure imaginary, and that seems completely reasonable to me, because if $b\neq 0$, then $a+bi$ cannot be real, but it is generally not pure imaginary. At least in algebra, the distinction is a useful one, as it is in geometry. I realize I may not always express myself as well as I should, and that, as editors, you're concerned with improving the language. I also realize I've been guilty of one or two "think-o's" that look really amateurish, but that doesn't mean I don't try to choose my words carefully, as I did here. In my opinion, using informal terms like "imaginary number" in a context where they can be easily confused with pure imaginaries detracts from the article and makes it look unprofessional. But that's just my opinion. Greg Woodhouse 09:50, 17 April 2007 (CDT)

I had a look in the history. Your version is fine, but a later edit completely changed the first sentence. In the old version, "imaginary number" means any number a + bi (with a, b real) where a is nonzero; in the new version, a has to be zero. That introduced the problem I was talking about. -- Jitse Niesen 23:08, 18 April 2007 (CDT)

I'm not sure what happened, but I believe I said that such a number is not real, but neither is it pure imaginary. Of course, it's possible that I didn't type what I was thinking. Greg Woodhouse 15:18, 20 April 2007 (CDT)

I reverted the intervening edit which changed the first sentence, so the article is now back to what you wrote. -- Jitse Niesen 21:27, 24 April 2007 (CDT)

rewritten

I have rewritten and expanded this article, and hope that the two different uses of "imaginary" are now described clearly enough. Moreover, I have added some details on related terms. Peter Schmitt 14:30, 1 January 2010 (UTC)