Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2005-12-18 07:57:41

krassi_holmz
Real Member

Offline

vector multiplicated by i

What will happen with the vector if we multiply it by

?


IPBLE:  Increasing Performance By Lowering Expectations.
 

#2 2005-12-18 08:01:42

John E. Franklin
Star Member

Offline

Re: vector multiplicated by i

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


igloo myrtilles fourmis
 

#3 2005-12-18 08:11:19

krassi_holmz
Real Member

Offline

Re: vector multiplicated by i

OK. Let the vector be 2D.


IPBLE:  Increasing Performance By Lowering Expectations.
 

#4 2005-12-18 08:12:50

krassi_holmz
Real Member

Offline

Re: vector multiplicated by i

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


IPBLE:  Increasing Performance By Lowering Expectations.
 

#5 2005-12-18 08:15:50

krassi_holmz
Real Member

Offline

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 (2005-12-18 08:18:14)


IPBLE:  Increasing Performance By Lowering Expectations.
 

#6 2005-12-18 11:24:39

John E. Franklin
Star Member

Offline

Re: vector multiplicated by i

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


igloo myrtilles fourmis
 

#7 2005-12-18 18:45:04

krassi_holmz
Real Member

Offline

Re: vector multiplicated by i

I use the following for italic

Code:

[i]italic[/i]

If I tell you it won't be interesting


IPBLE:  Increasing Performance By Lowering Expectations.
 

#8 2005-12-18 18:54:02

krassi_holmz
Real Member

Offline

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?


IPBLE:  Increasing Performance By Lowering Expectations.
 

#9 2005-12-31 10:25:14

God
Full Member

Offline

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).

 

#10 2005-12-31 10:39:34

krassi_holmz
Real Member

Offline

Re: vector multiplicated by i

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


IPBLE:  Increasing Performance By Lowering Expectations.
 

#11 2005-12-31 11:00:20

God
Full Member

Offline

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 (2005-12-31 11:00:54)

 

#12 2005-12-31 22:28:06

krassi_holmz
Real Member

Offline

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|+(i|y1-y2|))=sqrt(|x1-x2|-|y1-y2|)


IPBLE:  Increasing Performance By Lowering Expectations.
 

Board footer

Powered by FluxBB