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Where on the number line is i?

 
 
aperson
 
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?
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Type: Discussion • Score: 0 • Views: 640 • Replies: 4
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stuh505
 
  1  
Reply Fri 8 Sep, 2006 11:25 pm
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.
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markr
 
  1  
Reply Sat 9 Sep, 2006 12:54 am
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.
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aperson
 
  1  
Reply Sat 9 Sep, 2006 03:48 am
Cheers
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djjd62
 
  1  
Reply Sat 9 Sep, 2006 03:54 am
i can't draw a plane Crying or Very sad

i can draw a fairly reasonable representation of a boat or car
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