Do complex numbers exist in nature?

[OneWorldOneNumber]

Not even sure how to begin with something " imaginary" and build insight through questions on this, " seriously."

 

From my book on Elementary And Intermediate Algebra, page  584.

Talks about the ideas behind the use of a number that is a square root of -1 also referred to as i

 

Uhmmm, Ok.....So then " where did complex numbers come from then??

 

The page goes onto to mention how negative numbers do not have negative squared roots... Understood, however then it says:

 

Larger number systems that contain the " real number systems" " Real number - Wikipedia" is designed so that negative numbers do have squared roots.

Ok....... Who was this designer??? And why are Larger numbers able to do this???

 

Hope i made sense here...

 

Edited April 22, 2021 by OneWorldOneNumber

[Prometheus]

Are you OK with negative numbers? Do they exist in nature?

[joigus]

47 minutes ago, OneWorldOneNumber said:

Not even sure how to begin with something " imaginary"

"Imaginary" is just a word. Don't read too much into it. "Real" is just a word, don't read too much into it. "Exist" is just a word..., and so on. If a circle really exists, then complex numbers really exist. If a circle doesn't really exist, then complex numbers don't really exist.

Can things kind of exist to you, instead of really exist?

"Use" is a far nobler verb than "exist."

You can use complex numbers and understand many things with them as a tool.

[SergUpstart]

In nature, there are no numbers, neither natural, nor integer, nor fractional, nor real.... Numbers are our mathematical abstraction for describing nature.

And if we put the question like this, is there anything in nature that cannot be described without complex numbers, then yes, there is a wave psi function in quantum mechanics.

44 minutes ago, Prometheus said:

Are you OK with negative numbers? Do they exist in nature?

Electrical charges

[studiot]

1 hour ago, OneWorldOneNumber said:

Do complex numbers exist in nature?

Not even sure how to begin with something " imaginary" and build insight through questions on this, " seriously."

From my book on Elementary And Intermediate Algebra, page  584.

Talks about the ideas behind the use of a number that is a square root of -1 also referred to as i

Uhmmm, Ok.....So then " where did complex numbers come from then??

The page goes onto to mention how negative numbers do not have negative squared roots... Understood, however then it says:

Larger number systems that contain the " real number systems" " Real number - Wikipedia" is designed so that negative numbers do have squared roots.

Ok....... Who was this designer??? And why are Larger numbers able to do this???

Hope i made sense here...

 

Nothing nonsensical about your question  - many people have asked it over the centuries.

I don't think this is a speculation, however.
It is a straightforward mathematical question that deserves a straightforward mathematical answer, that you algebra book, despite its 600+ pages (Wow) probably doesn't offer you.

The very short answer is yes it does, but you need to know a little bit of electrical engineering.

In AC power engineering there are two quantities known as the real and apparent power in a circuit.

Put simply the real power is the power measured on a true RMS power meter and is the power an electric fire would draw from the mains.
It is calculated without using complex numbers.

Most other electrical devices draw (ie those with motors, flourescent tubes, transformers etc) draw what is known as apparent power which uses complex arithmetic to calculate the values. This is not an inefficiency of these devices it is inherent in their mode of operation.

It should be noted that there is a difference between imaginary numbers and complex numbers  - they are not the same and do not follow quite the same algebraic rules.

i is an imaginary number, not a complex number.

The term complex derives from the fact that it is in two parts, unlike the real numbers (and the imaginary ones) which have only a single part or are simplex numbers.

All complex numbers have a real part and an imaginary part so are a combination of two parts.

Complex numbers are written in the form (a + ib) (They also have other formats) which clearly demonstrates this 'a' is the real part and 'ib' the imaginary part and the + sign denotes the combination of the two.

But there are also 'complex'  number systems  that are composed of two real parts for example (a + √3b) called surds or extended real numbers.
In this case no imaginary parts are involved.

 

[swansont]

!

Moderator Note

Note that the OP has been banned as a sockpuppet of a previously banned member, but feel free to continue discussing. Just without their participation 

 

[Country Boy]

I remember reading "God created the counting numbers- all the rest is the creation of man" but, unfortunately cannot remember where or who to attribute it to.

At the time I thought, "Well, yes, it is easy to distiguish between one and two elephants, but what about one or two slime molds?  Are the counting numbers really so obvious?"

[Phi for All]

8 hours ago, Country Boy said:

"God created the counting numbers- all the rest is the creation of man"

That's hilarious, and SO ironic! It reminds me of a bumper sticker a friend of mine had made up: "I didn't get to be a starship captain by living in a fantasy world!"