complex numbers? (1 Viewer)

[selablad]

Sorry, I don't think this is in the right forum, but I don't know which to put it in anyway so...

Anyway, my maths teacher was telling us about how, when you're drawing normal numbers you put them on a number line, and how for complex numbers you plot them on a graph-looking thing (like with 2 axes). So my friend and I were wondering, what are the numbers that need to be plotted on 3 axes called, if you can even do this, and how do you get them? I mean you get complex numbers from i^2 = -1 so how do you get 3D ones?

I'm sorry if this is a really obvious question, I was just curious

 

[tommykins]

It's like the normal graphs, except the x axis is Re(z) and the y axis is Im(z)

 

[Sandchairs]

3d graphs are like the point x(2,4,6) 2 on the x axis, 4 on the y, 6 on the z
its a rectangular prisim if ur confused

this explains it
http://en.wikipedia.org/wiki/Z_axis

 

[Affinity]

you can't really have a 3 dimensional system, The next one up happens to be 4 dimensional called the quarternions
you have i,j and k

i^2 = j^2 = k^2 = -1

ij=k
jk=i
ki=j
ik=-j
ji=-k
kj=-i

you lose commutativity of multiplication here though.

 

[me121]

yeah, as just said you get to quarternions

 

[Affinity]

though it's hardly used except in computer graphics and as a curiosity.

If you learn a bit more about the complex numbers, you would see that they represent rotations/dialations in the 2 dimensional plane. and they can be represented by a 2x2 matrix with real entries.

the quarternions are similar in that they represent "rotations" in a 2 dimensional complex plane and can be represented by a 2x2 matrix with complex entries,

oh by the way, I lied when I said you can't have a 3 dimensional system... you can define a somewhat sensible (though alot less than the quarternions) system.

 

[behemoth100]

Haha this is not a rude comment but given this is a 3 unit forum, that post is pretty much completely useless. Not in terms of the world hehe, just to these 17 and 18 year old kids who haven't even heard of euler's formula .

After 2 years of uni I haven't heard of quartenions .

 

[behemoth100]

Sorry, I don't think this is in the right forum, but I don't know which to put it in anyway so...

Anyway, my maths teacher was telling us about how, when you're drawing normal numbers you put them on a number line, and how for complex numbers you plot them on a graph-looking thing (like with 2 axes). So my friend and I were wondering, what are the numbers that need to be plotted on 3 axes called, if you can even do this, and how do you get them? I mean you get complex numbers from i^2 = -1 so how do you get 3D ones?

I'm sorry if this is a really obvious question, I was just curious

Something not to be confused about :
Imaginary numbers: multiples of i (as you said the square root of negative 1)
Complex numbers: A number of the form z (<- called complex number) = a + ib
Where a and b are real numbers, and i is (-1)^1/2
e.g z= 5 +9i
z= pi - ei
A complex number as you can see has a Real part (the a ) and an imaginary part (the bi).
The imaginary part is graphed as the 'y axis' and the real part is graphed as the x axis.
So a complex number is made up of 2 parts. Real and imaginary. 2 axes.

If I understand your qs correctly, there is no '3D' number, as this woul d involve a number with a real component, an imaginary component, and some other form of numbering that doesn't exist. Its also important to see that we only graph a complex number to help put it in polar form, it doesn't really have a 'dimension'.

You can create a space with complex dimensions though. The cartesian plane is a space with 2 dimensions , one dimension is real, the other dimension is real and perp to the first. or 3 dimensions, one x one y one z, all perp. 4 spatial dimensions, graphically, is purely theoretical.

You can create a complex space with one dimension complex, and another dimension complex. Bit silly though, not useful in real world. Again theoretical.

Too add a final word, as I said we only graph complex numbers because they have 2 components. I suppose if you wanted to draw an analogy you could graph a real number in 2 dimensions as well. Have your x axis represent integer vaules 1, 2, 3 ,4 ,5... and your y dimension represent decimal places or 'fractions of integers. Thus 4.782 would be made up of 2 components, 4 ('x axis') and .782 which could be in the 'y axis'