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Use of Complex Numbers in Electromagnetism.

  1. Sep 20, 2007 #1
    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.

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  3. Sep 20, 2007 #2


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    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?
  4. Sep 20, 2007 #3
    In Electromagnetism you often deal with sinusoidal waveforms. The link between sinusoidals and complex numbers is done by Euler's 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 [tex]t[/tex] (the time) becomes equivalent with multiplying by [tex]j\omega[/tex], integrating becomes equivalent with dividing by [tex]j\omega[/tex], and the multiplication/division operations become more handy.
    Last edited: Sep 20, 2007
  5. Sep 20, 2007 #4
    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?
  6. Sep 20, 2007 #5


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    Never heard of "i EM theory", just as antonantal said, rewriting cos and sinus as complex numbers via Eulers formulas, you gain a lot.
  7. Sep 20, 2007 #6


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    'i EM-theory' was supposed to read 'in EM theory'.
  8. Sep 20, 2007 #7
    That's a typo... "*in* EM-theory". If you want to learn about complex numbers in EM, just learn about complex numbers in waves.
  9. Sep 20, 2007 #8
    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.
  10. Sep 20, 2007 #9


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