With this example, students can "feel" the emergence of imaginary component when something starts to resonate instead of just fading out. It makes for a nice demonstration in a classroom. It helps to convince that complex numbers are not some made-up constructs but a part of nature just as reals, and make up a much more coherent theory with nicer rules and less exceptions compared to real arithmetics.
Another more dry and technical use is in equation solving in general. For instance, solving for real roots of a real polynomial can be done through complex arithmetics with complex intermediate results. This still begs a question, where in real life you need to solve a cubic equation as an example but that's another story. So to study various factors we use transformation.
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- Complex Numbers With Applications.
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- Application of Complex Number in Engineering..
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Where are complex number used in the real world: Some examples are in cameras forming images, in x-ray crystallography used to determine the structure of molecules such as proteins, in MRI and CT scanners used in hospitals, in various forms of spectroscopy used to identify molecules and in lasers used to understand and predict their behaviour. I am afraid your conditions on what real utility of a mathematical object means is so strict as to render all applications of mathematics ridiculous.
Indeed, such a restriction soon leads us into philosophising about what is useful and what is not, what is real and what is not. Why should the compactness with which the complex numbers unify some elementary relationships and so effect easier methods of mathematical analysis not be counted as a real world application, since, as others have pointed out and you yourself probably knew they are used in the study of such periodic phenomena as the analysis of signals -- which has applications in the systems designed by engineers to convert between such signals?
For that matter why should the mechanical engineer who analyses vibrations not count it a real world application when it makes him able to predict in advance the effects of the vibration of his system on a structure?coineunewdeca.tk/hamilton-the-birmingham-of-canada.php
Applications of Complex Numbers - Mathematics Stack Exchange
So, I hope that you can see that the idea of what is useful, real, or applicable is very flexible indeed. Finally, let me comment on what I think the issue usually is with people finding it hard to see the practical utility whatever that means elsewhere of the complex number system: But gradually, our idea of number evolved to include things that are not quantities at least not in the usual sense of the term -- the discovery of antimatter is very, very recent, compared to the timeline of mathematical history in the original understanding of the term -- eventually with the discovery of other division algebras, which began with the quaternions of Hamilton, the concept of number became nebulous and is today best left as primitive.
In summary, the utility of a mathematical object should be judged in light of its nature and what it can model appropriately which may be far removed from the ordinary experience of the common man ; this nevertheless does not detract from its utility. The following is a personal opinion, but I think mathematics, no matter how rarefied and strange, is a kind of reflection of the world. I think the world is bizarre and strange, and that we have barely begun to understand and control it.
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Home Questions Tags Users Unanswered. Ask Question. PhD PhD 1, 5 18 Michael Hardy Michael Hardy 1. Therefore it is not unexpected for them to arise in situations involving trigonometric functions, such as waves and oscillations mentioned by Michael Hardy. A concrete example of their use is in phasors for example.
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I presume "one being the current" was meant. My response was this: Kamil Jarosz 4, 3 12 Peter Peter 1 3. Are you familiar with Quantum Electrodynamics? You are referring to the fields maintained by charges particles.
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Does it really state that protons, electrons, neutrons are particles, not waves? If they are particles, does each of them have strictly defined coordinates and speed at any moment? From the uncertainty principle, there is no way to simultaneously observe both a particles location and velocity. Not only that it's impossible to measure the coordinates - the "particle" just doesn't have them.
Particle without coordinates is not actually a particle, it's something else. Is situation the same in Quantum Electrodynamics? Does it really states that particles do have coordinates that's just impossible to measure? The whole point with my answer is that complex numbers are only for simplifying the applications - that there's actually no application that absolutely require them.
After all since complex numbers are constructed from real numbers in a relatively simple way too everything that can be done with them could be done without them as well. Why that shouldn't apply to linear filter design I can't see.
Application of Complex Number in Engineering.
At one time I had more analog filter design books than the number of filters I designed: Have a look at: Amzoti Amzoti Robert Israel Robert Israel k 23 This insight, like any mathematical ephiphany, suddenly has applications to lots of areas, such as Fourier analysis, digital signals and many of the other examples mentioned elsewhere.
YYC 1, 15 Allawonder Allawonder 1, 6 Finding the intersection of two line segments? Rotating an object around a point? Possible, but painful. Once you start dealing with angles and rotations, the notation starts to be really clumsy. Part of the reason is that you have to work with each coordinate separately, and you don't really see the connections between the coordinates and the angles. This all changed once we realized that the Complex plane https: Thus, when doing analytic geometry in 2D, instead of representing a point by a pair of reals, we can represent it by a single complex number.
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Home Questions Tags Users Unanswered. Applications of Complex Numbers Ask Question. Thank you for your time and thanks in advanced for your feedback. We are trying to remove them. Kevin Driscoll Kevin Driscoll 4 Roland Roland 4, 1 13 Thomas Thomas Eleven-Eleven Eleven-Eleven 5, 7 27 Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.