What Are Imaginary Numbers Used For In Real Life

SPECULATIVE SCIENCE

What use are imaginary numbers in the existent world? Do they take purpose or is it simply mathematicians having some fun ?

Bob Jones , Aberdeen Scotland

All numbers are imaginary (fifty-fifty "cypher" was contentious once). Introducing the foursquare root(s) of minus 1 is convenient because (i) all n-degree polynomials with real coefficients then have northward roots, making algebra "consummate"; (ii) it saves using matrix representations for objects that foursquare to -ane (such objects representing an important part of the structure of linear equations which appear in quantum mechanics, heat diffusion, optics, etc). The hottest contenders for numbers without purpose are probably the p-adic numbers (an extension of the rationals), and perhaps the expiry dates on army ration packs.
Michael Hall, Canberra Commonwealth of australia

Don't forget that maths is an invention, if you like the rules of a game by which nosotros play. Maths is NOT a science, it does non represent reality (or even attempt to) - it is a arrangement which but WORKS. It is designed for convenience. Since the roots of maths predate the complexity that led in much later on centuries to imaginary numbers, it is no surprise that later elaborations for functions originally unforseen proved problematic. Further: do numbers have a use in the "existent" world? Well, yeah, but plainly crucial (and well-established!) continuations, like algebra, have only THEORETICAL or abstract uses: which is, in upshot, the apply imaginary numbers take. Imaginary numbers run contra to common sense on a basic level, just you must have them as a system, and then they make sense: recall that nothing makes 2+2=iv except the fact that we SAY So. Same with imaginary numbers. The discomfort you experience is the clumsiness non between reality and the i series only betwixt the (deceptively named) "existent" series and its i counterpart. And if by "use" you mean awarding, I am sure plenty of mathematicians and physicists and engineers will swear to their importance.
M B Drennan, Oxford UK

On the contrary, purely real numbers only depict a perfect, simplified world in physics while imaginary numbers must be used to include the myriad complicating factors establish in the "real" earth. For example, the schoolhouse text-volume pendulum was a doddle, with nice real numbers and a swing which carried on forever. However, friction with the air causes damping of the motility so that it decreases over time, and the only mode to deal with damping is using imaginary numbers. Maybe it would've been better to characterization the types of number the other way around, or simply "plus-root" and "minus-root" numbers or something.
Mark Lewney, Cardiff EU

They are of enormous use in applied maths and physics. Complex numbers (the sum of existent and imaginary numbers) occur quite naturally in the report of quantum physics. They're useful for modelling periodic motions (such as h2o or light waves) equally well as alternating currents. Agreement circuitous assay, the written report of functions of complex variables, has enabled mathematicians to solve fluid dynamic problems especially for largely two dimensional issues where glutinous effects are small-scale. You tin can also sympathise their instability and progress to turbulence. All of the in a higher place are relevant in the existent globe, as they give insight into how to pump oil in oilrigs, how earthquakes shake buildings and how electronic devices (such as transistors and microchips) work on a quantum level (increasingly of import as the devices shrink.)
Gareth Owen, Crewe Britain

Ask any phisical scientist or engineer (mechanical, ceremonious or electrical) how they would get on without using the square root of minus one. They will tell yous near of our technology depends on it. For case, without using imaginary numbers to calculate various circuit theories, you lot would not be reading this on a computer.
G Baker, Ockendon, UK

Yes, electric engineers apply them as they are a mathematical representation of alternating current. They utilise 'j' to represent the square root of -one (unlike mathematicians who use 'i') since in electrical technology 'i' represents "current".
Campbell McGregor, Glasgow, United kingdom

Whilst being whimsical for an eccentric mathematician, imaginary numbers can exist very useful for solving engineering problems. On instance is if you lot have a pendulum swinging, it starts to slow down and eventually stop. If you want to work out the motion of the pendulum over a sure fourth dimension (ie derive a formula) then the best fashion to practice information technology is to utilise complex numbers.
Aidan Randle-Conde, Crewe UK

They have been used extensively in the latest Conservative party manifesto!
David Vickery, Croydon, UK

If you're talking about things similar the square root of minus ane, then they have all sorts of applications. For example, if I call back my physics (imprecisely) the two-dimensional number matrix formed by real numbers and multiples of "i" (i.e. sqrt-one) is a good approximation for the way electromagnetic waves collaborate between their electrical and magnetic components.
Richard, London, UK

Imaginary, or complex, numbers aren't much employ when adding up your shopping bill or working out your tax, (on 2d thoughts...) but they accept been a vital tool in the developement of mathematics. Equally an example, you probably wouldn't accept the weather forecast if it wasn't for imaginary numbers. Although forecast models don't use circuitous numbers themselves (though you may remember they exercise), the mathematical theories on which the models are based rely on them.
Raymond Lashley, Reading, United kingdom

They find ample application, along with all those sines, cosines and tangents and the rest of your high school math, in many areas of engineering such equally electronics and electrical engineering. Rather than wanting to actually evaluate the foursquare root of minus one it is handy to have something that when squared is minus i. It's best illustrated with a simple circle and sine wave.
Yard. Finn, Tulsa, OK USA

Lets accept a number of 3 + 4i 3 ------> is actually the horizontal component of the strength. iv -------> is actually the vertical component of the force. Complex numbers come up into place whenever 1 strength gets divided into two or more components due to inclination or any other reason. There are more that one manner an object can be inclined and thus more than one way these forces get divided into 2. The i, j and one thousand planes are a resultant of this. BINNOY http://visualizingmathsandphysics.blogspot.in/2013/06/what-is-purpose-of-complex-numbers-in_18.html
Binnoy. S. Panicker, Mumbai, Bharat

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