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Imaginary numbers

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Is it just me, or is this whole imaginary number stuff just a bunch of crap? I learned this in Algebra II class the other week. Now, my teacher is trying to apply it. What meaning will this have in my life? Don't get me wrong, I understand the concept...but, why do I need to know this?

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Well since you want to be a pharmacist, you'll need it to get into graduate school, but then won't need it at all :P

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It depends what you do. For instance, imaginary numbers are rather vital in certain areas of electronics.

 

You might as well say this of any topic that you won't directly use in your life (assuming you don't use them).

 

Bear in mind, of course, that the "imaginary" part is just the name and only idiots misunderstand this to mean that they don't exist.

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Imaginary numbers are important for all reasons mentioned.. AND to better understand the theory of mathematics. Believe it or not... there is a REAL problem when we cannot resolve a number because of the paradox it posses. My favorite (and most famous) imaginary number is the square root of -1, which is represented by a lower case i. what's interesting is that i can be manipulated mathmatically and make real numbers, but i is imaginary. And you find multiples of i to be non-real roots of many quadratic equations. So solving these requires knowledge of imaginary numbers.. and that means they are essential to elements of Calculus (applied to curves with imaginary solutions) and Algebra (the whole quadratic thing). Imaginary numbers will not help you in most professions, but then again.. there are a LOT of impractical things you are forced to learn.

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a root or a quadratic is where the line touches or crosses the x axis, if the quadratic has imaginary roots, it doesnt actually touch the x axis. so why the hell do we have to say it has a root? i didnt know there was equal rights for polynomials.

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Because imaginaries are solutions to the quadratic equation.

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i know there solutions, but if the quad doesnt touch the x axis, it doesnt really need solutions, why not just say the quadratic formula cannot be factorised?

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if imaginary numbers had never been created, then it would be accurate, and a hell of a lot more logical. and i wouldnt have had so much work to do in yr 12

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It's true that it would make straighforward quadratics easy... but if you remember the "Determinant", which is b^2 plus 4*a*c... where a,b,c are all three numbers of the quadratic. The determinant shows how many roots of the quadratic exist, and if you get a negative number, you know there are two imaginary root and none others... so that makes your job a lot easier because you can't solve the equation. If it weren't for imaginary numbers, you would not be able to determine this and would instead work tirelessly on the solution. OR when you used the Quadratic "formula" (the whole b squared plus or minus the square root of....) you will see the solutions.. and sometimes you get imaginary answers.

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Originally posted by bucks

i know there solutions, but if the quad doesnt touch the x axis, it doesnt really need solutions, why not just say the quadratic formula cannot be factorised?

 

It does if you have a 3 (or 4) dimensional graph with each set of axes being represented by an Argand Plane.

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Originally posted by MrL_JaKiri

It does if you have a 3 (or 4) dimensional graph with each set of axes being represented by an Argand Plane.

 

What's that?

 

Also, I've read somewhere on the Theory of Relativity, and faster than light travel.

 

Apparently travelling faster than light is imaginary as well:D

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Originally posted by NSX

 

What's that?

 

Also, I've read somewhere on the Theory of Relativity, and faster than light travel.

 

Apparently travelling faster than light is imaginary as well:D

 

Oh god, this sounds like Hawking. IGNORE HIM HE'S A MORON.

 

an argand plane is where one axis represents real numbers and the other imaginary. Just have 2 of those instead of 2 lines for the axes.

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Originally posted by MrL_JaKiri

 

Oh god, this sounds like Hawking. IGNORE HIM HE'S A MORON.

 

lol

Why's that?

 

Originally posted by MrL_JaKiri

an argand plane is where one axis represents real numbers and the other imaginary. Just have 2 of those instead of 2 lines for the axes.

 

So do the axes intersect each other?

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Originally posted by NSX

 

lol

Why's that?

 

 

 

So do the axes intersect each other?

 

Well, hawking isn't really all that respected because he dumbs all the science down in his books until it's actually wrong.

 

And the axes intersect eachother at 0, as will all axes, and are at right angles to eachother.

 

(Real x, imaginary x, real y, imaginary y)

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Originally posted by MrL_JaKiri

 

Well, hawking isn't really all that respected because he dumbs all the science down in his books until it's actually wrong.

 

Really?

My Physics teacher said it would be in layman's language; but I didn't know it went that far...

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Originally posted by eric

Is it just me, or is this whole imaginary number stuff just a bunch of crap? I learned this in Algebra II class the other week. Now, my teacher is trying to apply it. What meaning will this have in my life? Don't get me wrong, I understand the concept...but, why do I need to know this?

 

that is not such a good way to look at it. complex analysis will play an intregral part to finding a theory of the universe, if it exists. the joyce manifolds theorized in string theory are partially complex. complex variables also play a huge role in engineering.

 

 

and to the person who said that imaginary numbers are baloney basically, i dont think that is so. Gauss, one of the greats, proved that imaginary numbers must exist and have a logical backbone to it.

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Originally posted by MrL_JaKiri

Well, hawking isn't really all that respected because he dumbs all the science down in his books until it's actually wrong.

 

And the axes intersect eachother at 0, as will all axes, and are at right angles to eachother.

 

(Real x, imaginary x, real y, imaginary y)

 

that does not even deserve a reply

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can someone present a practical application for imaginary numbers?

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method of steepest descent is one, off the top of my head.

 

also fourier integrals, riemann-hilbert spaces, geez the list goes on dude

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Originally posted by blike

can someone present a practical application for imaginary numbers?

 

electrical engineering is the main one that i can think of, but there's quite a lot of others. it's also pretty important for various basic things like damped/forced harmonic motion (you can end up with a second order differential equation that requires complex numbers to provide a real solution).

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anything to do with harmonic motion is good, because you can represent sin(blah) with e(blah) saving wodges of time when integrating differentiating and so on.

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Guest Lynn
MrL_JaKiri said in post #17 :

 

And the axes intersect eachother at 0, as will all axes, and are at right angles to eachother.

 

(Real x, imaginary x, real y, imaginary y)

 

Sorry, I don't quite get it. 4 axes at right angles to each other, how could it happen in 3-dimentions? Would it be 4-dimentions then?

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