Use of Complex Numbers in Electromagnetism.

[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.

 

[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?

 

[antonantal]

In Electromagnetism you often deal with sinusoidal waveforms. The link between sinusoidals and complex numbers is done by Euler's[/PLAIN] 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.

 

[Himanshu]

And also there is lot of different problems i EM-theory, are there any perticular problems you want to solve?

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?

 

[malawi_glenn]

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?

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.

 

[Astronuc]

And also there is lot of different problems in EM-theory, are there any perticular problems you want to solve?

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

 

[genneth]

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?

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

 

[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.

 

[malawi_glenn]

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.

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