Reply
Fri 8 Sep, 2006 11:10 pm
If I were to draw a plane, with a real number n being at (n,0), where would i, 2i, -i and -2i go?
You can define any coordinate system you want. Judging by the fact that you mentioned a plane, I will make the assumption that you want to use the standard basis, where x=[1,0,0], y=[0,1,0], z=[0,0,1] (you have infinite options though).
You can only plot coordinates (eg, points) if you have a value for each vector that makes up the basis. So you need an x,y, and z value to plot something in this.
"i" has an i value of 1, and you didn't specify x,y, or z...so it can't be plotted!
If you define your coordinate system to be xyzi, then you could plot a coordinate like [0,0,0,1] which would correspond to 0x+0y+0z+i. But this is 4 dimensional so you couldn't really draw a good picture of it, unless you wanted to use time to visualize the 4th dimension in which case it would be a movie.
Typically, complex numbers are plotted on a plane with the x-axis representing the real component and the y-axis representing the imaginary component.
The complex number a+bi would be represented by the point (a,b). The imaginary numbers you asked about are equivalent to the complex numbers:
0+1i
0+2i
0+(-1)i
0+(-2)i
This should be enough information to figure out where they would be plotted on the complex plane.
i can't draw a plane
i can draw a fairly reasonable representation of a boat or car