- #1

- 58

- 5

- B
- Thread starter SHASHWAT PRATAP SING
- Start date

- #1

- 58

- 5

- #2

etotheipi

Gold Member

2020 Award

- 3,157

- 2,113

You're right! You can look at how Spivak defines complex numbers, as a pair ##(a,b)## along with the definitions ##(a,b) + (a,d) = (a+c, b+d)## and ##(a,b) \cdot (c,d) = (a\cdot c - b\cdot d, a\cdot d + b \cdot c)##. The ##x+iy## notation is recovered by setting ##i = (0,1)##, and ##(a,0) = a##. There's nothing very strange about this at all. And imaginary numbers are just a subset of ##\mathbb{C}##, of the form ##(0,b)##.

Historically, mathematicians have a tendency to be skeptical about new developments, hence why "imaginary" was introduced as a bit of a diss.

Historically, mathematicians have a tendency to be skeptical about new developments, hence why "imaginary" was introduced as a bit of a diss.

Last edited:

- #3

- 15,561

- 7,720

The name originally was due to skepticism and has stuck. There is, however, an important distinction between real and complex/imaginary numbers in physics. Complex numbers tend to be part of the mathematical machinery, but measurements are always real numbers. You can measure an angle ##\theta##, but you can't do a measurement and get an imaginary angle ##i\theta##.

This is hard-wired into Quantum Mechanics, where measurements are the eigenvalues of Hermitian operators - and these operators always have real eigenvalues. There are other important operators in QM that have complex or imaginary eigenvalues, but these explicitly are not measurable quantities.

- #4

fresh_42

Mentor

- 14,118

- 11,372

Not what, whom! It was René Descartes 1637. The reason was very likely, that the complex zeros of polynomials, for which the imaginary numbers were first needed, couldn't be seen in their graphs.

- #5

- 58

- 5

Here comes an important point- IMAGINARY NUMBERS are Imaginary but their existance is not Imaginary they really exist. it was imaginary in the sense as it was left to the people's imagination to imagine a solution to the square root of negative numbers and use the letter

So,IMAGINARY NUMBERS are Imaginary but their existance is not Imaginary.they are "imaginary" but not in the sense of fantasy or fiction.It is just the same word being used differently.....

Please tell me have I understood it correctly.....

- #6

hutchphd

Science Advisor

Homework Helper

- 2,291

- 1,597

I prefer a more teleological approach: is the concept useful? Of course then one needs to define "useful"

- #7

fresh_42

Mentor

- 14,118

- 11,372

You did not. The correct version is in my post #4. Descartes used it 1637 for the first time. Mathematicians at this point in time were still busy to solve polynomial equations. Imaginary numbers occurred in the formulas of Italian mathematicians like Cardano, Tartaglia or Ferrari a century ago. Descartes, however, coined the namePlease tell me have I understood it correctly.....

It is not helpful to fantasize some speculative explanations if history is as clear as in this case.

- #8

- 58

- 5

My question is not how , its why did he coined the name Imaginary if these numbers really exists.Help me.Descartes, however, coined the nameimaginary.

please help me i am confused i want to know why were these numbers called imaginaryI prefer a more teleological approach: is the concept useful? Of course then one needs to define "useful

- #9

fresh_42

Mentor

- 14,118

- 11,372

Look up Helmuth Gericke: Geschichte des Zahlbegriffs. Bibliographisches Institut, Mannheim 1970, p. 66. and the references therein.My question is not how , its why did he coined the name Imaginary if these numbers really exists.Help me.

Again, and for the third time: If you want to know why Descartes named it so, you will have to read the original occurrence.

The question has been answered. Speculations are meaningless, so this thread will be closed.

https://en.wikipedia.org/wiki/Discourse_on_the_Method

https://gallica.bnf.fr/ark:/12148/btv1b86069594/f5.image

Last edited:

- Last Post

- Replies
- 13

- Views
- 5K

- Replies
- 4

- Views
- 3K

- Last Post

- Replies
- 5

- Views
- 6K

- Last Post

- Replies
- 2

- Views
- 832

- Last Post

- Replies
- 14

- Views
- 3K

- Last Post

- Replies
- 27

- Views
- 11K

- Last Post

- Replies
- 4

- Views
- 9K

- Last Post

- Replies
- 9

- Views
- 4K

- Last Post

- Replies
- 6

- Views
- 817

- Last Post

- Replies
- 11

- Views
- 3K