View Full Version : Simple high school math question

Chrono_Wanderer

9th October 2003, 19:03

Ok, I think I am the smallest MURCer here, so please don't laugh at my stupidity in Math. (I am still doing Gr 12)

Anyways

I am just wondering if the complex plane containes number in only 4 dimensions, or is it infinite?

Sorry for such a stupid post. But I asked the calculus teacher and apparently he doesn't know :rolleyes:

Helevitia

9th October 2003, 19:16

Sorry, I don't know your answer, but I wanted to tell you that my highest math is pre-algebra. I've had to learn more math over the years because of my job and it has been tough! Now I am Learning C and I am finding that my limited math skills aren't hindering me to bad.

Dave

the main lobe

9th October 2003, 19:31

Not sure what is meant by 4 dimensions in a complex "plane". I think 2 dimensions whenever I think plane. I am fairly certain though that a complex vector space can have infinite dimension.

Chrono_Wanderer

9th October 2003, 20:08

Originally posted by the main lobe

Not sure what is meant by 4 dimensions in a complex "plane". I think 2 dimensions whenever I think plane. I am fairly certain though that a complex vector space can have infinite dimension.

LOL, i think I used wrong terminologies.

Actually I meant "does complex numbers contain numbers in infinite dimensions, or is it jsut restricted to 4D"

Well, AFAIK, vector spaces can have infinite dimension theoretically speaking.

lol, I think you have answered my question, but when you say

"complex vector space" does that mean like (a, b), (c, d), (e, f) or is it numbers like "4i" (i.e. sqrt of -4)

sorry for my stupidity, because I just started my geometry course, and haven't gone into any vector geometry yet. And worse of all, physics is not in this semester :|

@Helevitia: Must be though for you! Glad its easy for you tho! I think education in your time and my time is very different, so highest math = pre-algebra must be very normal. Things really changed, these days everybody is taking Calculus and stuff. Anyways, glad that you are making great progress in C! I think I will learn C this summer (should't take long because Java has almost same syntax as C coz Java is essentually based on C)

Reason I need to learn C is because I am planning to go into comp engineering, and rather than in most comp sci course, engineering probably prefer C over java, hehe. :)

Well, best of luck in learning C, it must be an interesting language :) (hey Helevita, are you an engineer or a programmer?)

the main lobe

9th October 2003, 20:28

Basically imaginary vector spaces are the same as real number vector spaces...all the same rules apply. (Although you are probably not familiar with them...I surely wasn't familiar with the term vector space when in H.S.) The only difference is that that imaginary numbers are included. Like i4 or -i8, or 4+i8. Going into any engineering field (especially electrical or computer) you will learn that imaginary numbers are very important. Reactance of an inductor (jwl) or a capacitor (1/(jwc)) for example are imaginary. You'll also be replacing i with j so you do not confuse sqrt(-1) with current which takes the symbol i.

Most useful math site I know of,

http://mathworld.wolfram.com/

GuchiGuh

9th October 2003, 20:54

this reminds me that i failed my maths mid-semester by 1 mark....:mad:

But seriously the lecturer is a f***king bastard!!! his marking is so f***ked up! i did one WHOLE page of working to find eugenvalues of a matrix and got the numbers wrong in the end and he f***king gave me 0 (zer0, nill, null) marks!:mad:

but yes...chrono_wanderer..:

........actually i have no idea what you mean....i think my english never improves...

Helevitia

9th October 2003, 22:01

Originally posted by Chrono_Wanderer

@Helevitia: Must be though for you! Glad its easy for you tho! I think education in your time and my time is very different, so highest math = pre-algebra must be very normal. Things really changed, these days everybody is taking Calculus and stuff. Anyways, glad that you are making great progress in C! I think I will learn C this summer (should't take long because Java has almost same syntax as C coz Java is essentually based on C)

Reason I need to learn C is because I am planning to go into comp engineering, and rather than in most comp sci course, engineering probably prefer C over java, hehe. :)

Well, best of luck in learning C, it must be an interesting language :) (hey Helevita, are you an engineer or a programmer?)

I'm an engineer. Actually, so far, C isn't really as hard as I thought it would be. It is very logical which works best for me since I am a logical person. The best part is, I don't really need to know the math so much as how to put together the formula :) Luckily the guy I sit next to at work has his masters in computer programming :D He is very helpful to me and I have definitely learned a lot from him.

It's funny because I work with numbers all day long and I think that alone helps me out tremendously.

Dave

Chrono_Wanderer

9th October 2003, 23:30

GRRRRR!!!! Too many smilies and lost all my typing to the cyberspace :mad:

Anyways, I will make this "short" ;):

@the main lobe. Thanks for the info! Seriously! You just changed the way I look at this thing, and I discovered I did something really stupid all these years. Ok, don't laugh, but I always thought real = x-y plane and complex = anything outside. Obviously I am seriously flawed because all along I have only been restricted in 2-space. (Besides, the class is just starting to understand what limits are :rolleyes:) Anyways. If I am thinking correctly, there is a complex domain in x-plane, a complex domain in y-plane, etc... infinite planes. Basically, complex number is only a field, not a dimension. If this is correctly, then I feel really stupid :p

Ok, I think I can see why they call these "imaginary numbers"... I think its because we can't make a direct reference to this with real life things... they are simply not... countable. But that also raises a question for me, why do we need it for?

AFAIK most electrical/computer engineering studies need the students to know this inside out. So what's the deal with capacitor reactance? Is it like calculating the uF value for caps? But I don't really see it, should reaction time be "countable"? LOL, I am a poor lost soul :p

And I feel dumb.

Thanks againf the info, that really helped me A LOT!

@GuchiGuh: That sucks :( And hey! Stop scaring me like that! I was hoping that I can at least relax for 1 more year before getting tortured! LOL *jk*

@Helevitia: LOL, well, you have the logic, but apparently I don't lol. Can you spare some logic this way please? (I will pay for the shipping!!!!) Anyways, isn't that's what "theoretical works" are all about? You know the stuff when you don't know you know it youself. :P

edit: about the link, the main lobe, Bookmarked! :) Thanks for that too!

Gurm

10th October 2003, 04:51

Complex numbers (numbers including imaginary components) have, as a general rule, the same dimension as their non-complex counterparts.

Therefore, 4i has the same dimension as 4. One dimension. And a "plane" in complex space, (ix, iy) has the same dimensions as a plane in regular space (x,y).

- Gurm

VJ

10th October 2003, 05:33

Yes, but you have additional complexity (quaternions)

http://www.lboro.ac.uk/departments/ma/gallery/quat/intro.htm

1. i is square root of -1

2. j is second square root of -1

3. it kan be proven that k=i*j is a third square root of one, not equal to i or j.

Commonly, only i is used, which results in a 2D environment, adding j results in 3D and adding k results in 4D.

(real numbers are 1D: the real axis)

I don't think there are higher dimensions above this, as i,j and k are the only roots of -1; but I could be wrong about this...

Jörg

Gurm

10th October 2003, 05:52

Jorg,

You're CONFUSING THE BOY. ;)

- Gurm

Technoid

10th October 2003, 06:07

Math is intentionally confusing ;)

VJ

10th October 2003, 06:14

Originally posted by Gurm

You're CONFUSING THE BOY. ;)

(hmm, I get that remark a lot... :confused: )

Even so, I think this was his question: he mentions 4 dimensions, and a plane... So, if you only use i, you have the 2 dimensional plane. If you consider i,j and k, you are working in a 4D space which cannot be referred to as a plane.... :)

To my knowledge, there are no extensions higher than 4D for complex numbers...

Jörg

Gurm

10th October 2003, 06:22

"Plane" in and of itself implies 2 dimensions. :)

- Gurm

VJ

10th October 2003, 07:05

Yes, but as Chrono also mentioned 4 dimensions (or infinite ?) I figured he wanted to know if the extensions go beyond the quaternions (and that "plane" was a typo).

Jörg

Kooldino

10th October 2003, 07:42

Originally posted by Chrono_Wanderer

Ok, I think I am the smallest MURCer here, so please don't laugh at my stupidity in Math. (I am still doing Gr 12)

Anyways

I am just wondering if the complex plane containes number in only 4 dimensions, or is it infinite?

Sorry for such a stupid post. But I asked the calculus teacher and apparently he doesn't know :rolleyes:

Sheesh, you don't know the answer to THAT? HAUGH HAUGH HAUGH. I LAUGH at your stupidity in math.

dbdg

10th October 2003, 08:07

I remember dealing with complex numbers and eigan (sp) values and vectors at A-Level.

Shame I can't remember anything but being in that actual class. now. :eek:

Have to agree with Kooldino though, are you really that stupid that you had to ask. :D

Gurm

10th October 2003, 08:38

I'm just trying to figure out what "high school math" requires more than passing familiarity with imaginary numbers. ;)

- Gurm

Duty

10th October 2003, 10:53

Now my head hurts... I'm still trying to forget this stuff ;).

Jeff

SpiralDragon

10th October 2003, 11:12

math and i are mortal enemies... :D

Chrono_Wanderer

10th October 2003, 11:41

Ok, seriously :rolleyes: all we learn about complex number is "square root of -1" lol.

And ok, Gurm, I think I am kidna gettting this. I think its sort of like...

for the x-domain (not plane, plane is 2d byitself. it used plane before b/c it was a misuse of words)

x-domain of real numbers

x-domain of i

x-domain of j

x-domain of k

for the y-domain

y-domain of real numbers

y-domain of i

y-domain of j

y-domain of k

etc... goes on infintely

so there is only 3 "fields" for complex numbers? (i, j, k) Or is there anymore?

Or am I at least in the right direction?

@Others! Hey, don't laugh dude! At least I am trying to understand this crap. lol. If I don't get these straight before university, I will probably get kick out the first week, rather than get kick out the first month :D

Chrono_Wanderer

10th October 2003, 11:47

Originally posted by Gurm

I'm just trying to figure out what "high school math" requires more than passing familiarity with imaginary numbers. ;)

- Gurm

Actually the irony is you don't really need to know what imaginary numbers are in my HS. But blah. what I am doing right now at school are: introductory Euclidean proves for my discreet math course, and don't laugh, but "first principle" in calculus lol.

So far I think I am doing well :) (note "I think" :D)

the main lobe

10th October 2003, 11:57

typically when using imaginary numbers. The ordinant(vertical axis) is marked imaginary, and the absicca(horizontal axis) is the real axis. (2,2i) is where you'd usaually find (2,2)...and imaginary numbers are just as real as real numbers. Gotta go to class (optical information processing)...yippee.

Chrono_Wanderer

10th October 2003, 17:12

oh right, of course lol. i guess otherwise its kinda hard to have an imagine value for an independent variable. :)

So,optical info processing, sounds interesting!

Again,thanks a lot for the info :)

VJ

12th October 2003, 08:12

Originally posted by Chrono_Wanderer

[B]for the x-domain (not plane, plane is 2d byitself. it used plane before b/c it was a misuse of words)

x-domain of real numbers

x-domain of i

x-domain of j

x-domain of k

for the y-domain

y-domain of real numbers

y-domain of i

y-domain of j

y-domain of k

etc... goes on infintely

so there is only 3 "fields" for complex numbers? (i, j, k) Or is there anymore?

I think there are only three; the link I posted previously

http://www.lboro.ac.uk/departments/ma/gallery/quat/intro.htm

The way to obtain i, j and k are on the page. I don't think there are more, as this would imply there be other than these three roots of -1.

But I am not sure what you mean with the x and y domains. It looks like you want to have complex numbers as coördinates in a 2D space ? :confused:

Normally, the real axis is X, the axis for i usually is Y, thus resulting in a 2D plane. Adding j and k results in having to model complex numbers in a 4D space. (don't forget: a complex number has 4 "fields", a real number is just a special case of a complex number) A number a+bi+cj+dk is then positioned at coordinates (a,b,c,d). All 4 axes are real axis so to speak (a,b,c and d are real numbers), but as they each have a different dimension, togheter they result in the 4D complex space.

Jörg

Liquid Snake

13th October 2003, 14:39

I'm in 12th grade also and have no idea what you're talking about :alien: I learned about complex numbers a couple of years ago but I've probably forgotten most of it :D

I can tell you what capacitive reactance is, though. Basically, it's a capacitor's resistance to AC. AC will cause the capacitor to continuously charge and discharge, which has an affect on the current, called reactance. I think my definition is kind of crappy though, so maybe someone like Greebe can chime in with a better definition :)

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