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

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Imaginary numbers are defined as numbers whose square results in a negative value, represented as a real number multiplied by "i," the square root of -1. For example, 5.29i is an imaginary number, while complex numbers combine real and imaginary parts, such as 3.5 - 22.6i. These numbers are essential in physics, particularly in describing oscillations, as they provide a compact mathematical representation that simplifies complex problems. Their utility extends to various physical phenomena, including sound, AC circuits, and light in absorptive media. The introduction of complex numbers has been particularly significant in quantum mechanics, where they are commonly used to describe physical systems, making equations more manageable.
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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