Author Topic: imaginary numbers  (Read 3003 times)

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Offline Spoil9Topic starter

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imaginary numbers
« on: February 10, 2009, 09:51:01 PM »
Quick question for those with experience in this department...
How much are imaginary numbers used in the real world? I understand that they are important for working with AC signals and other things, but is this something that is used everyday, or once in a while?
Just wondering.
Thanks.
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Offline TrickyNekro

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Re: imaginary numbers
« Reply #1 on: February 11, 2009, 02:42:16 AM »
I don't really get, what you are asking here...
These numbers are supposed to give some answers to various things real numbers can not....
Apart from AC there are used alot in waves.... electromagnetic and so....
This is because an oscillation has two mathematic forms....
It can be either expressed with a trig function or a imaginary function (using Euler transformation)



Basically, they don't really have a meaning.... they are just tools that help us do graphs and calculations.....
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Offline alllie

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Re: imaginary numbers
« Reply #2 on: February 11, 2009, 06:28:54 PM »
as i understand it they're very important, especially when dealing with anything representing waveforms. for that reason i would venture to say they're used everyday

Offline paulstreats

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Re: imaginary numbers
« Reply #3 on: February 11, 2009, 08:58:29 PM »
Im not really up on pure math or anything but as i remember, imaginary numbers are created by multiplying a number by i (where i is the square root of -1 ?). I think the way to derive and use i is by the use of complex numbers or pairs of numbers.

 Pairs of numbers dont usually have any real world relevance but they are great for things with 2 properties that can be counted individually but are still interlinked. an electromagnetic field for example has an electrical property and a magnetic property at the same time. these properties can be both viewed individually or they can be viewed as pairs of numbers where 1 property has a direct relevance to the other. (almost like adding or viewing another dimension). I suppose that in some cases that when 1 of those properties changes, then the other property must also change, occasional meaning that its product becomes its own number summed in some way with a supposed negative number square. (the imaginary number set). In normal numbers this doesnt happen but with complex pairs 1 property changing can force an equation that doesnt obey the regular mathematical system.

 I am quite hazy on this... 

Offline Spoil9Topic starter

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Re: imaginary numbers
« Reply #4 on: February 11, 2009, 10:37:27 PM »
Thanks guys. I understand what complex numbers are and the basics of how to use them, I'm just starting to really hate them and was hoping that this was something that I would not see again after I graduated. But seeing how they are used so much with waves and such I don't see that happening. Especially if I want to work with power generation and/or EV's.
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Offline paulstreats

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Re: imaginary numbers
« Reply #5 on: February 12, 2009, 01:22:18 PM »
hi,

i found this website this morning http://www.math.toronto.edu/mathnet/answers/imaginary.html it offers a good explanation of imaginary numbers, how to use them and why they are so difficult for us to comprehend

Offline Asellith

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Re: imaginary numbers
« Reply #6 on: February 12, 2009, 01:46:44 PM »
I work as a radio engineer and I never use imaginary numbers. You need to understand the concept but the math is generally now used. Depends on what you get into. If your a power engineer working on new ways to transmit high voltage maybe or creating your own antennas then maybe. Once you specialize in an area that needs them then you'll understand them enough it will seem way easier. I might be a bad example of an engineer as my job doesn't involve much math at all. In my experience unless your on the cutting edge doing things that have never been done before or designing new things the really high level math take to much time and someone made a program to do it and your company paid for it.
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Offline cosminprund

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Re: imaginary numbers
« Reply #7 on: February 12, 2009, 02:04:17 PM »
Since when are complex numbers "high level math"? My god, if that's high level...

Offline Spoil9Topic starter

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Re: imaginary numbers
« Reply #8 on: February 12, 2009, 09:17:26 PM »
I work as a radio engineer and I never use imaginary numbers.......In my experience unless your on the cutting edge doing things that have never been done before or designing new things the really high level math take to much time and someone made a program to do it and your company paid for it.


I edited your quote a little, but by far that is the best answer I have gotten about anything related to future EE stuff that I may be doing.
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Offline HDL_CinC_Dragon

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Re: imaginary numbers
« Reply #9 on: February 12, 2009, 11:10:27 PM »
I work as a radio engineer and I never use imaginary numbers.......In my experience unless your on the cutting edge doing things that have never been done before or designing new things the really high level math take to much time and someone made a program to do it and your company paid for it.


I edited your quote a little, but by far that is the best answer I have gotten about anything related to future EE stuff that I may be doing.
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Offline cosminprund

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Re: imaginary numbers
« Reply #10 on: February 13, 2009, 02:14:25 AM »
I work as a radio engineer and I never use imaginary numbers.......In my experience unless your on the cutting edge doing things that have never been done before or designing new things the really high level math take to much time and someone made a program to do it and your company paid for it.


I edited your quote a little, but by far that is the best answer I have gotten about anything related to future EE stuff that I may be doing.

Neh... It's probably the one you wanted to hear.

I'd ask Asellith if he could get throw EE school without learning all that boring math. Even if you don't use the stuff every day or every week or ever, once you understand it, if you ever need it again, you can take out that old dusty math book and apply that formula, because you understand it. Even if you don't use the math itself every day, you'll use things you used that math to understand.

I'd rephrase your question. I'd ask the people that have a EE degree if they think math played an important role for them. If math was/is important, learn the darn thing and stop looking for excuses not to. I'll say this again: Complex numbers are only complex in name and aren't close to being "high level math".

Offline 4by4

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Re: imaginary numbers
« Reply #11 on: February 13, 2009, 08:56:41 AM »
As a retired EE, I can say that EE requires a lot of math both in school and in the profession. EEs are kind of like applied physicists, and physics is basically mathematical theories. Specifically, physics theories are differential equations. The branch of math used by engineers most is "Analysis" or the theory of functions, which includes calculus, and analysis includes lots of functions of a complex variable such as Fourier Transforms, Laplace Transforms, Z-Transforms, etc. These are basic for analyzing circuitry and electromagnetic wave theory (Maxwell's equations). They are tools for solving differential equations. Analysis of functions of a complex variable also is basic for quantum mechanics, and quantum mechanics is the basis for all semiconductor physics. That includes many of the sensors used in robotics such as optical and infrared detectors.

Another area of math used a lot by EEs, especially in artificial intelligence and image processing is statistics, AKA functions of a random variable. Most of image processing and image interpretation involves "clustering" - finding statistically optimal groupings of measurements.

I would say most practicing EEs don't spend a lot of their time writing and solving equations, unless they are researchers. But they use the textbook solutions to write their software models and signal processing algorithms, so they have to understand the theory. Most engineering involves translating existing theory into some real world application. So it's more looking up stuff in the textbooks and literature. But you have to know where to look and what to look for.

Offline Asellith

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Re: imaginary numbers
« Reply #12 on: February 13, 2009, 09:55:36 AM »
maybe I was unclear in my statement. I didn't say not to try and understand them and give up. I just don't see the point in worrying about it. I understand the use of imaginary numbers and what they are used for but could I off the top of my head solve some of the problems I use to in college.... NO. College was like a massive download of information and experience that gives me a head start on learning new things or as 4by4 said applying them. I use my numerical methods book more then anything. I don't care how to do a complex calculation. What I care about is making my microcontroller do it.

So to answer the original question imaginary numbers are not used that much and when they are it is seldom just crunching numbers to solve random problems like your experiencing now in college. However solving all those problems will help you the next time you need to understand the concept so it is important but don't get think that college life is anything like having a real job.

Also I didn't mean to imply that imaginary numbers where "high level" But the last time I did any type of complex signal analysis it had imaginary numbers in it.

and just to defend myself... If my computer fails I either fix the computer or grab the textbooks I have on shelves above my desk and get the job I have to do done. When your in college do the work get the grades but in reality the guy next to you who has a 4.0 but doesn't know what a capacitor actually looks like is less of an engineer.
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Offline Spoil9Topic starter

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Re: imaginary numbers
« Reply #13 on: February 13, 2009, 04:55:43 PM »
cosminprund-
It is the answer I was hoping to hear. Although I may not have phrased it the way I was thinking it, 4by4 and Asellith did answer my question...
taking into account that every job is different, and that there are many, many aspects of EE jobs, what are the chances that I will be sitting behind a desk somewhere doing some work and randomly I'll have to pull out a piece of paper and a pencil and start crunching complex numbers, Eulers identity, converting it all to polar form and etc and what not?
I have sat through lectures, studied and gone to tutors to learn and understand this stuff. I am not looking for a way out. I just can not wrap my head around something if I can not see how it is useful in real life and so far every prof. has said that it will be "one day".

This is just how I am. When I was in grade school, I had a hard time learning long division because my teacher would/could not explain why I needed to know it other than "what happens if your calculator batteries die?" I now understand it, and understand how it is used later on with solving functions and I am glad I learned it, but at the time I didn't know what I know now so it was hard to learn.

On that note, I understand that learning this helps solve other problems later on, but if I can't see some examples of that work, I find it hard to learn. Of course this is prob more than anyone cares to know about me, I just wanted to explain that I am not trying to skip out on learning this, just trying to get a better understanding than... "you'll use it one day"
I apologize and in the future I will spend more time trying to explain my questions better so as to avoid these confusions.
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Offline 4by4

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Re: imaginary numbers
« Reply #14 on: February 14, 2009, 09:55:30 AM »
By the way, that explanation at toronto.edu seems way too complicated. The imaginary number "i" is just a way of representing a rotation through 90 degrees. Does a rotation through 90 degrees exist? Obviously it does.

Offline colorclocks

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Re: imaginary numbers
« Reply #15 on: February 14, 2009, 02:30:41 PM »
I was the same way at one point in my education.  I found that I had a harder time learning things that I suspected I would never need to know, so I didn't learn them as well as I could have.  The fact that they did not seem important while I was "learning" them, made them weakly held, and not well connected, in my brain.  If you don't jump in with both feet, you brain notices this.  It believes you, when you think what you're learning is not important,and it responds by not connecting the new information securely, and by not associating it widely.

Later, I found that I had to relearn those things because they were stopping me from making progress in something that I did care about.  So I had to try to learn both at the same time, and that's harder to do.

Students always think a field of study is useful or not depending on whether someone else will ever make them solve a textbook problem in that field.  Students are wrong about this, and the reason they get this wrong is that they don't come to understand what education is for, until they think they are done with it.  Ideally, students would learn how their brain works first, and then try to stuff things into it, but that's not the way we teach.

The more things you learn, the more "hooks" you have in your brain on which to hang other things you might someday want to learn, and the more associations you will be able to make between learned ideas and new ideas.  It's totally not about someone in the future expecting you to turn some crank.  It's about you having the ability to understand and manipulate ideas that you will care about, and to make associations that other people's brains have not already made between ideas.  It's about expanding the range of ideas that are accessible, and therefore potentially useful, to you.

I think the only way to waste your time in school is to not attach importance to the things you are learning.  If you learn something well, your brain will find a way to use it.


« Last Edit: February 14, 2009, 02:46:05 PM by colorclocks »

Offline Tomas

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Re: imaginary numbers
« Reply #16 on: February 14, 2009, 03:05:52 PM »
I must say, I havent graduated yet (im on my last semester), but I've used imaginary numbers ALOT during my education. And I really dont find it that hard. Its mostly i^2=-1, and thats it (some different approaches in the different uses, but they all use that single rule). I really do see the point of knowing this, especially if you are thinking about working with communications. So learn it damnit, its NOT difficult.
« Last Edit: February 14, 2009, 03:08:42 PM by Tomas »

Offline 4by4

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Re: imaginary numbers
« Reply #17 on: February 15, 2009, 08:08:11 AM »
You're right i^2 = -1 is all there is to it. If you want to visualize that, consider if you rotate a vector by 90 degrees twice it's facing 180 degrees in the opposite (-1) direction.

Offline Admin

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Re: imaginary numbers
« Reply #18 on: February 18, 2009, 01:56:53 AM »
Imaginary numbers are very important for analyzing analog signals (like sine waves, etc).

That being said, I've never needed imaginary numbers outside of class . . . all my electronics are digital so don't require calculus/trig to analyze/design the signals . . .

 


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