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

• Jack
In summary, imaginary numbers are represented by the product of the square root of -1 and a real number. They are used in physics as a mathematical tool to simplify and compact difficult problems, especially in phenomena involving oscillations and systems with planar geometry or translational symmetry. Their use has increased with the introduction of quantum mechanics. They are also jokingly referred to as numbers you give to someone you don't want to talk to.

#### 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 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.

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

## What are imaginary numbers?

Imaginary numbers are a type of complex number that is expressed as the product of a real number and the imaginary unit, denoted by i. They are used to represent the square root of negative numbers, which cannot be expressed as a real number.

## How are imaginary numbers used in physics?

Imaginary numbers are used in physics to represent quantities that have both a magnitude and a direction, such as alternating current in electrical circuits or the wave function in quantum mechanics. They are also used in vector calculus and differential equations to solve problems in electromagnetism and mechanics.

## Why are imaginary numbers used in physics?

Imaginary numbers are used in physics because they provide a useful mathematical tool for solving problems that involve complex quantities. They allow us to represent physical phenomena that cannot be described using only real numbers, such as the behavior of waves and oscillations.

## What is the difference between real and imaginary numbers?

The main difference between real and imaginary numbers is that real numbers can be represented on a number line and have a physical meaning, while imaginary numbers cannot be represented on a number line and are used as mathematical tools to solve equations. Additionally, real numbers can be positive, negative, or zero, while imaginary numbers are always expressed as a multiple of i.

## How do you perform operations with imaginary numbers?

To perform operations with imaginary numbers, you use the same rules as for real numbers, but with the addition of the imaginary unit i. Addition and subtraction are performed as normal, while multiplication and division are done by following the rules for multiplying and dividing complex numbers.