Application of Complex Numbers

  1. 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. jcsd
  3. 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?
     
  4. 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
     
  5. Hurkyl

    Hurkyl 16,090
    Staff Emeritus
    Science Advisor
    Gold Member

    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!
     
  6. Complex numbers sometimes provide a quicker way to solve certain questions, which is always a plus.
     
  7. Complex numbers aid to solve certain integrals that seems impossible like this one:

    [tex]\int_{-\infty}^{\infty} \frac{1 + x^2}{1 + x^4} \, dx [/tex]

    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.
     
  8. A Concrete Example

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

     
  9. Mark44

    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.
     
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