can you give me a real world example where imaginary numbers might be used?

Question

I need an example so that I can understand how algebra plays a part in our everyday lives.

Answer 1

Imaginary numbers are used extensively in quantum mechanics, to describe the motion of electrons around an atom.

Also, they are used in crystallography to define crystal structure.

Answer 2

There is a process coming from the calculus of functions of a complex variable (where the values taken by the variable are complex, having a real and an imaginary component) called a conformal mapping, which used to be heavily used in physics to understand the laminar (non-turbulent) flow of a fluid. Which lead to engineering applications in ship and aircraft design. But I get the impression that those are not as commonly used anymore, because you get more specific results through computer modeling.

Complex numbers are also useful for understanding heat flow in a surface: in nice cases, I remember solving the equations involved via a simplification involving another property of functions of a complex variable. In some other cases we used the conformal mapping I mentioned before.

The quantum physics involved in modern chemistry, and which is behind the engineering problems with nanotechnology, is based on an equation where one side multiplies an imaginary quantity by "i" to get a real quantity.

So, at least in physics, chemistry, and some engineering, there is a need to use (and understand) imaginary numbers.

Answer 3

This applies specifically to electrical circuits. In an electrical circuit, depending on the components in the circuit and whether or not the circuit is AC or DC, imaginary number play a part in determining the overall impedance (a fancier word for resistance) which exists within the circuit.

In the above description in an application of an AC circuit, for example, a component of impedance with respect to a capacitor would be described in part by the term "j" over "omega" times "C". omega is the frequency component, as the frequency grows larger and larger the impedance gets smaller and smaller. Think of it this way, which is smaller, one over ten or one over 100? One over 100 of course is smaller.

Imaginary numbers are used in this manner as a way of measuring the resistance in an electrical circuit.

Answer 4

Wikipedia has an absolutely fantabulous explanation for this, under "applications of imaginary numbers". Let's see if I can dig it out for you...
Ok, here we go
Scroll down to about the middle of
http://en.wikipedia.org/wiki/Imaginary_numbers
(begin quote)
[edit] Applications of imaginary numbers
Despite their name, imaginary numbers are as "real" as real numbers.[2] (See the definition of complex numbers on how they can be constructed using set theory.) One way to understand this is by realizing that numbers themselves are abstractions, and the abstractions can be valid even when they are not recognized in a given context. For example, fractions such as ⅔ and ⅛ are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones. Similarly, negative numbers such as − 3 and − 5 are meaningless when keeping score in a US football game, but essential when keeping track of monetary debits and credits[1] (or yards gained on a play in the same football game).

Imaginary numbers follow the same pattern. For most human tasks, real numbers (or even rational numbers) offer an adequate description of data, and imaginary numbers have no meaning; however, in many areas of science and mathematics, imaginary numbers (and complex numbers in general) are essential for describing reality...
(end quote)
Good stuff. You can read the rest here..
http://en.wikipedia.org/wiki/Imaginary_numbers

Answer 5

The other posters are doing a fine job here answering your question. To toss in my two cents, let me just say that imaginary numbers come up so much in theoretical physics that I am starting to believe the universe itself is imaginary.

Answer 6

Imaginary numbers are used in developing some fractals.

Answer 7

There are many instances in physics (especially in the fields of electricity and magnetism). The article below should help to outline a few of these.

Answer 8

Imaginary numbers are, by definition, not real numbers. They are numbers that only exist in the imagination of people like you and me. However, by understanding imaginary numbes you will gain a better understanding of real numbers. It is easier to say, for example, that every possible quadratic equation has two roots (or one repeated root) than it is to say that some quadratics have two roots, some have one root and some have none at all.

Answer 9

Electrical engineering comes immediately to mind. They talk about it a little in this article:

http://en.wikipedia.org/wiki/Imaginary_number

Answer 10

Reactance calculations while designing electronic circuitry. How's that?