# Use of Complex Numbers in Electromagnetism.

1. Sep 20, 2007

### Himanshu

I read in an article that the theory of Electromagnetism makes use of Complex Numbers. How are the tools and tricks of Complex Numbers used in Electromagnetic theory. I just wanted to understand the basics of this connection of Complex Numbers and Electromagnetism and figure out if this technique could help me to solve problems more efficiently.

Thanks.

2. Sep 20, 2007

### malawi_glenn

Maybe they talked about Möbius transformations ? Do you know the name of the "technique" ? And also there is lot of different problems i EM-theory, are there any perticular problems you want to solve?

3. Sep 20, 2007

### antonantal

In Electromagnetism you often deal with sinusoidal waveforms. The link between sinusoidals and complex numbers is done by Euler's[/PLAIN] [Broken] formula. In this way you can write the sinusoidals as complex exponentials, a technique which simplifies very much the calculations.
For example differentiating with respect to $$t$$ (the time) becomes equivalent with multiplying by $$j\omega$$, integrating becomes equivalent with dividing by $$j\omega$$, and the multiplication/division operations become more handy.

Last edited by a moderator: May 3, 2017
4. Sep 20, 2007

### Himanshu

No particular problems. 'i EM-theory', as you call it, is a fairly new stuff for me. I just wanted to know its basics. It would be great if you could find me a reference to it.

And by the way, what's Möbius transformations?

5. Sep 20, 2007

### malawi_glenn

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

Never heard of "i EM theory", just as antonantal said, rewriting cos and sinus as complex numbers via Eulers formulas, you gain a lot.

6. Sep 20, 2007

### Staff: Mentor

'i EM-theory' was supposed to read 'in EM theory'.

7. Sep 20, 2007

### genneth

That's a typo... "*in* EM-theory". If you want to learn about complex numbers in EM, just learn about complex numbers in waves.

8. Sep 20, 2007

### Himanshu

I thought that 'i' stand for iota for complex numbers.

Anyway, Möbius transformation is way above my head.

"complex numbers in waves", that's a good connection. Thanks genneth.

9. Sep 20, 2007

### malawi_glenn

Möbuis transformation you use to solve laplace equation in an easier way, and that equation comes up in certain field theories =)