What are imaginary numbers and how and why are they used in physics?

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Discussion Overview

The discussion centers around the concept of imaginary numbers, their definition, and their applications in physics. Participants explore the mathematical properties of imaginary and complex numbers, as well as their relevance in various physical phenomena, particularly in oscillations and quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Imaginary numbers are defined as real numbers multiplied by "i", the square root of -1, with examples provided such as 5.29i and complex numbers like 3.5-22.6i.
  • Some participants suggest that imaginary numbers are a useful mathematical tool for describing physical phenomena, particularly in damped oscillations, which are relevant in various natural processes such as sound and AC circuits.
  • Another viewpoint posits that imaginary numbers may actually be the 'natural' numbers for describing the physical world, as they allow for a more compact representation of complex systems, especially in contexts involving oscillations and planar geometry.
  • Complex numbers are noted to simplify equations and are particularly significant in quantum mechanics, where they are commonly used.
  • A humorous remark is made about the term "imaginary numbers," suggesting a non-serious interpretation, which is countered by another participant emphasizing the age of the original poster.

Areas of Agreement / Disagreement

Participants express varying interpretations of the role and significance of imaginary numbers in physics. While some agree on their utility as mathematical tools, others contest the nature of their application and relevance, indicating that the discussion remains unresolved.

Contextual Notes

The discussion includes assumptions about the audience's mathematical background and does not resolve the differing opinions on the foundational nature of imaginary numbers in physics.

Jack
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What are imaginary numbers and how and why are they used in physics?

Please could you try and make your answers as simple as possible and bear in mind that I have not even finished my GCSE course in maths yet.
 
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Imaginary numbers are represented as some real number multiplied by the number "i", which is a representation of the square root of -1. So 5.29i is an imaginary number. There are also complex numbers, made up of a real and imaginary part, like 3.5-22.6i.

The number i pops up in many relations. eix=cosx+isinx for instance.

Their uses are many. One example of their use is in damped oscillations. You might think that damped oscillations are a pretty narrow topic, but many things in nature work that way - sound, AC circuits, light in an absorptive medium etc.

That's about all I'll say. I could go on and on...but I won't.

Njorl
 
Originally posted by Jack
What are imaginary numbers and how and why are they used in physics?

Please could you try and make your answers as simple as possible and bear in mind that I have not even finished my GCSE course in maths yet.

Imaginary numbers are all those numbers whose square is a negative real numbers. All this number can be represented by the product of the square root of -1 (usually written as i or j in engineering literature) and a real number. The sum of a real number (positive square) and of an imaginary number is called a complex number. This are the numbers that are used in physics.

Their use is mostly a very useful mathematical tool (this is a disputed subject since there is also who believes that they are actually the 'natural' numbers to use to describe the physical world). Their introduction allows to compact two parameters into one pretty much like using a 2D vector and vector calculus. There is a large amount of very powerful theorems that allows to simplify difficult problem with real number, passing to the complex ones.
Example of this are all phenomena involving oscillations since their complex description is way more compact than the real one -even though it has some limitations. All description of physical systems that display some kind of planar geometry or traslational symmetry can also benefit from this representation since equations get a simpler form. The use of complex number in physics received quite a boost with the introduction of quantum mechanics where complex numbers are the standard while real ones are somewhat exceptional and appear only in what is measurable.

If it is not clear ask more about it...
 
Stop teasing the kid. Imaginary numbers are numbers that you give to girls that you never want to actually have a telephone conversation with.
 
You evil git, he's only 6
 

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