What Are the Best Sources and Theories on Complex Numbers?

[sitokinin]

I've been attending at high school and I have some ideas about complex numbers. I shared my thoughts with my math teacher. He decided to search. I want to make sure if none have thought them so I need some information about complex numbers. Could you offer me some written sources and the theories about it? (except the web address of wolfram)

 

[arildno]

Welcome to PF!
There are oodles of books dealing with complex numbers, and all the fun you can do with them.
As an example, Bak&Newman's "Complex Analysis" is one book, there are tons of others.
I would suggest you go into the homepages of some "University Press" (for example, "Harvard University Press" or "Oxford University Press" ("Springer-Verlag" is another publishing company)
Loads of textbook-names will appear on their lists; it wouldn't hurt hunting down a few
of those.

 

[tongos]

thats interesting! good luck

 

[sitokinin]

Thanks! However I've been living in Turkey (: So the University Press you suggested can be a little problem.

 

[arildno]

I am 100% sure there are excellent universities in Turkey.
In all probability, at least the larger ones, will have an associated University Press.
(Publishing books primarily aimed at students)
Maths is an international language; what you will learn about maths (and complex numbers) in Turkish, will also be valid internationally.

So, check up what's available in your native language first (I'm sure there are plenty of good textbooks in Turkish)

 

[sitokinin]

Yes! I'm going to try to speak with some math professors here. But I guess I should know some academic things that are over the high school if I want to get what excatly I want (; Beacuse here, education is being performed with English books. Maybe I should know some English terms about it.

 

[matt grime]

Mathematicians do not steal each others' ideas. IF you post them here someone will be able to tell you about them. Please do not get your hopes up, the chane that you have something original (as opposed to just novel) is very small.

 

[arildno]

If you feel a bit insecure about conveying your ideas to complete strangers, you should approach a local math professor. Stealing ideas from others is just about the worst offense a professional scientist/mathematician can commit, it goes against the very ethos of research.
No self-respecting professional would dare to commit this crime, so you really ought to present your ideas to someone knowledgeable in the field.

Also remember that as long as you possesses evidence of PRIORITY, you are the one who will be regarded as the originator of an idea.
Posts here at PF (and, not the least, your teacher's testimonial!) are such evidence, so you should consider this a safe enough place to expound a bit.

However, as matt grime also noted, steel yourself as follows:
"Most probably, what I've thought out is either well-known or dead wrong; it is only a slim chance that I might be right AND having found out something new&important".

This is not said in order to belittle you, or dismiss your ideas out of hand, but is simply a conclusion drawn from experience:
In the 20th century, virtually NOTHING has been added to maths from individuals who haven't studied maths at least for a few years at university level.
(Ramanurjan might be a counter-example, who, however, do not invalidate the general trend).

Modern maths is so rich and encompassing, so that to learn the necessary foundations of today's problems actually requires years of intensive study I severely doubt you are old enough to have gone through.
However, it on this level that original, creative research (usually/invariably) has its starting-point.

Again, this is NOT said in order to dismiss your ideas out of hand, but that assuming you've hit upon something correct&valid in respect to complex numbers (and I have no reason of doubting you're correct yet), then you are in all probability TOO LATE
(someone else have beaten you).

 

[matt grime]

There a few well known cases of 'amateur' break throughs, and these are mainly in combinatorial number theoretic areas.

And I strongly back up Arildno's comment, and I'm sorry I didn't make it clearer, that it is quite likely you have found something correct, but the sheer volume of research and its difficulty to do originally, means that quite possibly someone will have done it already. But it should be considered a good sign that you've thought about it independently.

Also, please note that even if it is genuinely new then where to publish it is a question to consider carefully. THere is a difference between, say, professional mathematical publications where the method is what counts, and amateur recreational mathematical puzzles, where you'd put, for example, a novel solution to a (numerical) problem.

If you wish you can pm me privately (I am a mathematician, and an algebraist, so it would raise eyebrows if I were to suddenly write somethine about complex numbers) and I can tell you in what category (innovative research, novel idea, or well known idea) you idea lies.

 

[arildno]

I would like to emphasize the importance of matt grime's comment here:
"..But it should be considered a good sign that you've thought about it independently.."

I would like to give an example from PF:
I was very much impressed of a young poster here who ON AN EXAM had developed what is known as "Taylor Series" without having known about it earlier.
(He was asking if these series were known/of some use)
Although Taylor series has been around for the last 300 years or so (and hence, alas, no novelty), it still shows an impressive talent and creativity to rederive it wholly by your own efforts.

If your own results are somewhat of this type, consider it to be a personal SUCCESS, not a failure!

 

[cire]

https://www.physicsforums.com/showthread.php?t=56771

 

[Tide]

When you "publish" your new ideas in a public forum you have no reasonable expectation that all observers will recognize your rights to the material. By presenting them on a public message board you are, in effect, placing them in the public domain. Moreover, many internet forums require that members agree to grant the site copyright of all material submitted.

 

[sitokinin]

Actually I wasn't afraid of snatching my ideas. I don't want to write here as long as I'm sure! Anway, some mathematicians had already thought it (: Maybe next time...

 

[master_coda]

When you "publish" your new ideas in a public forum you have no reasonable expectation that all observers will recognize your rights to the material. By presenting them on a public message board you are, in effect, placing them in the public domain. Moreover, many internet forums require that members agree to grant the site copyright of all material submitted.

Of course it's important to remember that even if you place something into the public domain it doesn't mean that other people can take credit for your work. Copying another persons work without giving that person due credit would still be considered plagarism.

 

[sitokinin]

Well, my idea about; if Z=x+yi, then how can we define (x+yi)^i ? I know how I can define (a+bi)^(c+di), but I'm coerced while I'm replacing ''i''

 

[matt grime]

If you know a general formual when the exponent is c+id, why not use it when c=0 and d=1?

 

[sitokinin]

Yes, i used, but I don't know how to use the concept of arg(Z)

 

[Tide]

Copying another persons work without giving that person due credit would still be considered plagarism.

That was basically my point. Plagiarism exists!

 

[master_coda]

That was basically my point. Plagiarism exists!

Of course it does. But if someone steals your ideas before you make them publically available than it will be a lot harder to accuse them of plagarism.