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*complex numbers.*

This is a translation made by me from a book for absolute beginners like me. Isn't this description...complex? I mean they are not more complex than real, natural, irrationals...Or are them?.

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In summary, complex numbers are numbers that have two axes, like real numbers but with different names. They were first identified by Euler in 1777 and are used in many different ways than real numbers.

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This is a translation made by me from a book for absolute beginners like me. Isn't this description...complex? I mean they are not more complex than real, natural, irrationals...Or are them?.

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See the references in

https://www.physicsforums.com/threa...ary-if-they-really-exist.996269/#post-6419479

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Thanks. This night owl who is me has get something to look at.

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- imaginaire - french - Descartes 1637
- imaginär - (swiss) german - Euler 1777
- imaginarium - latin - usual scientific language back then
- вообража́емый - russian - Euler was in Saint Petersburg, and the russian word starts with a "w", but they spoke french at the Tsar's court
- imaginary - english - irrelevant in that context

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The numbers have been known long before Euler, but not called complex. It takes ##\mathbf{i} ## to see why they are complex (latin for closely related or connected), namely ##\mathbb{R} \oplus \mathbf{i} \mathbb{R}##: You tie two real numbers into a pair which is a new

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I guess it is as complex as I want. Ah...in euskera is irudikari

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Google says imajinarioa, which I think make sense, because the word is probably taken from another language into basque, and all others around are latin languages.mcastillo356 said:I guess it is as complex as I want. Ah...in euskera is irudikari

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Google...

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I can also offermcastillo356 said:Google...

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I think it comes form the fact that complex means consisting of more than one part, real and imaginary.mcastillo356 said:Isn't this description...complex? I mean they are not more complex than real, natural, irrationals...Or are them?.

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Complex numbers, imaginary numbers also need one axis.mcastillo356 said:

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I still think that the invisibility of imaginary zeros in a polynomial equation ##p(x)=0## or specifically in ##x^2+1=0## was the reason Descartes coined the term imaginary. Gauß observed the possibility of the representation in a plane, which is complex in the sense of

Wikipedia has some interesting remarks on the history of the terms:

https://en.wikipedia.org/wiki/Complex_number#History

I haven't checked whether all claims are referenced, so some caution is due.

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I've written it too quickly; I meant complex numbers like ##a+bi##, for example, need a plane to show them graphically, clearly. I'm I wright?mcastillo356 said:

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mcastillo356 said:I mean they are not more complex than real, natural, irrationals...Or are them?.

What is in a name? That which we call a complex number by any other name would behave the same.

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But it would be a far different world if we had to use the Montague axis and the Capulet axis.

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But we could call an Argand diagram Verona.hutchphd said:But it would be a far different world if we had to use the Montague axis and the Capulet axis.

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Small typo, OP: the roots of ##x^2+1##.mcastillo356 said:In 1777 Euler set up the notation ##i## to identify any roots of ##x^2-1##, which are indistinguishable, and verified ##i^2=-1##.

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gleem said:What is in a name? That which we call a complex number by any other name would behave the same.

hutchphd said:But it would be a far different world if we had to use the Montague axis and the Capulet axis.

Objection! From my link above:Ibix said:But we could call an Argand diagram Verona.

If one formerly contemplated this subject from a false point of view and therefore found a mysterious darkness, this is in large part attributable to clumsy terminology. Had one not called +1, −1, √−1 positive, negative, or imaginary (or even impossible) units, but instead, say, direct, inverse, or lateral units, then there could scarcely have been talk of such darkness. - Gauß

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