In what real world situation will I use imaginary or complex numbers (like )?
They just seem so abstract and, er ... imaginary. Do engineers or computer technicians ever use them?

In what real world situation will I use imaginary or complex numbers (like )?
They just seem so abstract and, er ... imaginary. Do engineers or computer technicians ever use them?
They (actually, complex numbers) are an essential mathematical tool in most areas of engineering.
A good BBC radio programme from some time back: BBC  BBC Radio 4 Programmes  In Our Time, Imaginary Numbers
Complex numbers along with vectors provide a bridge between geometry and algebra, so we get all sorts of very mathmatically rigorous extra modeling tricks out of it.
One such is the anlysis of simple harmonic motion where complex numbers can be regarded as diplacement. Useful in electronics for studying oscilations.
Basically, imaginary numbers provide for "imaginary dimensions" in geometrical analytical situations.
Why the interest?
One could argue that nought is an imaginary number as it has no value but is capable of making other numbers bigger just by presenting them together..nought is not a value , just a concept but it is still incredibly powerfull
Okay, I understand how they might represent "imaginary" dimensions.
And another question. Why is it called the imaginary unit?
So as a unit does that signify the "imaginary" kind of number, as in . As if we would call the reals ?
Exactly right. One way to think of it is...
Consider the "number line"; zero in the middle, +ve numbers to the right; ve numbers to the left:
n .... 2 1 0 +1 +2 .... +n
Those are the "real" numbers.
Now rotate the number line 90deg anticlockwise. Now you have:
+n
.
.
+2
+1
0
1
2
.
.
n
These are the imaginary numbers.
Now you can treat these as coordinates on a 2D plane; the "complex plane". Any complex number can be represented by a position on the plane (r,i).
Now we can see that multiplying by a real number, stretches/moves along the real plane (multiplying by a negative number "flips" by 108deg).
The clever thing is that multiplying by i rotates a point by 90deg. Multiplying by a complex number is a combination of these operations (possibly rotating by an arbitrary angle).
Now, any position on the complex plane can also be represented by a distance from the origin (0,0) and an angle (phase). This is why complex math is so useful for signal processing.
Oh okay. So . I find that cool.
So the unit is the most fundamental sense of quantity? I know our numerical digits (0, 1, 2...) aren't absolute, because of the base systems. And numbers only describe the unitary quantity, I guess.
[QUOTE=pipster;296722]Hmmmm... Depends on your definitions of "nothing" and "something". That is the trouble with language, it can lead to all sorts of ambiguities like that. That's why mathematics depends on formalising the definitions of things. If by "nothing" you mean zero (or the empty set), then this is a real mathematical vlaue that can be treated as any other. Whether that makes it "something" or not depends on what you mean by "something"
My education in basic maths just stopped short of studying complex numbers, but I was interested in them and also imaginary numbers such as (i) the square root of minus one.
In particular I was fascinated by the fact that complex and, of course, imaginary numbers were not simply abstract mathematical entities, but had very useful practical applications. I fondly believed this showed the profound links between mathematics and the real world but was also an illustration of the famous quote, by Haldane, about the universe, or reality, being not only stranger than we imagine but stranger than we can imagine.
I have to say that I was slightly, but not completely, surprised when I watched a recent BBC television programme introduced by the mathematician, and Oxford professor, Marcus du Sautoy.
In this programme, which was one of a series, du Sautoy declared that complex, and hence imaginary numbers, were extremely useful, but not essential, mathematical tools that made a number of mathematical operations much less cumbersome and time consuming.
I think that is true of everything beyond addition!
It is also true that you could write all software in binary. It is just so much easier when you have C++ and an extensive library of highlevel functions.
Doing the math of GR using just arithmetical operations would be possible but even more difficult than it is using shorthand like tensors, etc.
Imaginary numbers are the closest thing to pure fabrication of what we already know. Using them with equations offers usual problems more solvable than what would otherwise not have otherwise been solved.
Take the basic idea of catapulting a negative unit, like it has a family of complex numbers, "ï". Subunits of negative values where positive integers failed. The problem with using numbers is realising the limit of their absolute entity as a unit, divided, multiplied, and so on. Complex numbers accept the limitations of real numbers. Then they go beyond those confines.
Tell me. Why does 1 x 1 = 1? Any way you can......
Because multiplying by 1 is "flipping" from going one direction on the number line to going the other way (a rotation of 180º on the complex plane). Doing that twice gets you back where you started.
Similarly, multiplying by i is a rotation of 90º in the complex plane. Doing that twice is a rotation of 180º, which is the same as multiplying by 1; in other words i x i = 1.
Also a note on multiplying by 1. Since multiplication is iteration of addition/subtraction, multiplying by 1 is a number minus itself then minus itself again.
1 minus 1 minus 1 is +1, which is just like flipping the sign.
So it's nothing really special there. is interesting because it yields an entirely different kind of number. . And is just one :P
That's one way of trying to explain it.
Another way: think of two negative axes though, right angles to one another; multiple them both out to get the surface area. It would be "1" as the concept of a surface area, not an axis, right?
If one is to use mathematics geometrically, one needs to be consistent, right?
Last edited by theQuestIsNotOver; December 23rd, 2011 at 02:45 AM.
Let me give you the definition of real numbers set of all rational and irrational numbers are called as real numbers. Imaginary numbers and infinity are not real numbers. We use real numbers to measure continuous quantities. The decimal numbers with an infinite sequence of digits to the right of the decimal point, are also real numbers.
Never mind about the two questions.
I'm still surprised imaginary numbers are used in realworld situations. Most unexpectedly finance and marketing.
One example is i = sqrt(1). Without this number, the polynomial x^2 + 1 has no zero.
Last edited by marnixR; January 2nd, 2012 at 02:52 PM. Reason: deleted spam link
Well, it's no so much an example but more of a definition (though not a very good one: is usually preferred)
True, but why would that matter? Is it required that every real polynomial of degree has at at least 1 root and at most roots?Without this number, the polynomial x^2 + 1 has no zero.
PS I am being a little unfair, but I seem to be asking you to to prove the Fundamental Theorem of Algebra, a nontrivial task
Last edited by marnixR; January 2nd, 2012 at 02:54 PM. Reason: deleted quoted spam link
your question is quite perfect .Even i have never thought this where is use of this imaginary number and also one question like that why peime numbers and what it's use .Even wre also use it and do examples of prime numbers .But no one know why do this .What it's use in feasture
Prime numbers are used in a number of places. One important one is encryption based on the prime factorization of large numbers. So, it is easy to encrypt and decrypt a message when you know the prime factors. It is hard to break the code because this would require factorizing a large number (the key) and finding the prime factors of a large number is hard.
Hi strange ,
It's amazing to know about the prime numbers tha they are used for encrypting .But i want to ask whether it is possible to decrypt it with these numbers using prime factors .The main thing is these are used for this purpose and what is a prime number in math are used in such purposes .So please tell us how this is used in encrypting some how to me .Thanks .
There is a lot of detail (too much, maybe?) here: RSA (algorithm)  Wikipedia, the free encyclopedia
This might be a simpler explanation: How Public Key Cryptography (PKC) Works (I haven't read that page though)
I am very eager to know the whole scinario of the Cryptography and the use of a list of prime numbers to be used in it to encrypt and decrypt .Thanks for the source you have given .I have gone through it and want more information regarding that .So please hel if you can provide me some more details .Thanks again for the reply .
You will have to be more specific about what you want to know. The Wikipedia page on the RSA algorithm is pretty complete.
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