# Application of Complex Numbers

1. Dec 29, 2004

### danne89

Hi! I'd a look at complex numbers and can't understand how they can be applied to "the real world". Can anyone give me some concrete examples, please. Or a site that does.

Danne

2. Dec 29, 2004

### danne89

Oh, woop! I now saw the thread a bitter down. But I think it question why, and this thread "what can I do with it". By the way, you can't delete threads anymore, or?

3. Jan 5, 2005

### robert Ihnot

Well, maybe this will help. Gauss proved that every equation of nth degree has n roots. This means the equation X^2+1 has two roots. However, it does not cross the X-axis. Thus the roots, +i and -i represent extensions of the number system. A reference on this is: http://www.uncwil.edu/courses/mat111hb/Izs/complex/complex.html [Broken]

Last edited by a moderator: May 1, 2017
4. Jan 5, 2005

### Hurkyl

Staff Emeritus
Complex numbers can be interpreted as being the combination of a phase (aka angle) and a magnitude. Thus, they're useful for describing things that are well described by a phase and magnitude. They're useful even when you only care about phase!

5. Jan 5, 2005

### daster

Complex numbers sometimes provide a quicker way to solve certain questions, which is always a plus.

6. Jan 6, 2005

### MiGUi

Complex numbers aid to solve certain integrals that seems impossible like this one:

$$\int_{-\infty}^{\infty} \frac{1 + x^2}{1 + x^4} \, dx$$

Complex numbers also appear in very differential equations, like the wave equation or the heat equation...

The problem is that we can't imagine it easily.

7. Jan 6, 2005

### NeutronStar

A Concrete Example

This is from an old post I made a while back that gives a concrete example of a complex quantity.

8. Nov 3, 2009

### Staff: Mentor

If I'm remembering my mathematics history correctly, complex numbers gave rise to the concept of vectors. It's no coincidence that complex numbers in rectangular form can be added and subtracted in exactly the same way as vectors in the plane.