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#1 2005-12-17 08:57:41

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

vector multiplicated by i

What will happen with the vector if we multiply it by

?


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#2 2005-12-17 09:01:42

John E. Franklin
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Registered: 2005-08-29
Posts: 3,566

Re: vector multiplicated by i

Is this a 2-dimensional vector?
What is the coordinate system?


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#3 2005-12-17 09:11:19

krassi_holmz
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Registered: 2005-12-02
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Re: vector multiplicated by i

OK. Let the vector be 2D.


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#4 2005-12-17 09:12:50

krassi_holmz
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Registered: 2005-12-02
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Re: vector multiplicated by i

It isn't so inportant what is the coordinate system.


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#5 2005-12-17 09:15:50

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: vector multiplicated by i

But let

v=ai+bj
(here i is vector, not (-1)^(1/2)! (-1)^(1/2) must be italic i)

Last edited by krassi_holmz (2005-12-17 09:18:14)


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#6 2005-12-17 12:24:39

John E. Franklin
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Registered: 2005-08-29
Posts: 3,566

Re: vector multiplicated by i

Refresh my memory.  What happens to the function y=x if you multiply
it by :italic(i)


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#7 2005-12-17 19:45:04

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: vector multiplicated by i

I use the following for italic

[i]italic[/i]

If I tell you it won't be interesting


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#8 2005-12-17 19:54:02

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: vector multiplicated by i

OK. First try to myltiply one point with coordinates {x,y}.
What will happen?
The answer is {ix,iy}. So?


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#9 2005-12-30 11:25:14

God
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Registered: 2005-08-25
Posts: 59

Re: vector multiplicated by i

So it exists in a complex 4-D coordinate system but only exists at the origin on a 2-D real system where the origin of the vector is (0,0).

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#10 2005-12-30 11:39:34

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: vector multiplicated by i

So the vector multiplicated by i becomes a vector with negative length!


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#11 2005-12-30 12:00:20

God
Member
Registered: 2005-08-25
Posts: 59

Re: vector multiplicated by i

The length (aka. magnitude) of the vector is still it's absolute value.

So for example, if you had a vector <1+i, i-1>, the absolute value of your x component is sqrt(2), the absolute value of your y component is sqrt(2), and so the length of the vector is 2.

Last edited by God (2005-12-30 12:00:54)

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#12 2005-12-30 23:28:06

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: vector multiplicated by i

I think you are right. But in Minklovski's 2D space the length between two points (x1,y1) and (x2,y2) is
L=sqrt(|x1-x2|²+(i|y1-y2|)²)=sqrt(|x1-x2|²-|y1-y2|²)


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