 # Square root of minus one sonhouse Posers and Puzzles 27 Oct '07 13:46
1. 28 Oct '07 17:18
Originally posted by sonhouse
THAT I know: Complex numbers are inherently involved with alternating current and RF, you have to use complex #'s to solve problems in current flow and voltages, say on an RF open wire feedline for instance, the current sine wave and the voltage sin waves are not in sync and require complex #'s to solve the real energy exchange, absorption or emission of RF ...[text shortened]... ameters into Mathcad or other software pacs and don't have to do the math by hand any more.
In quantummechanics it helps reduce the amount of calculating to be done.

Complex exponents are way easier to deal with than a bunch of sines and cosines.
2. 28 Oct '07 17:20
Originally posted by TheMaster37
In quantummechanics it helps reduce the amount of calculating to be done.

Complex exponents are way easier to deal with than a bunch of sines and cosines.
Not only that but in QM complex numbers are an essential part of theory. They are not just a recipe for quick calculus.
3. 28 Oct '07 17:32
Thank you all for answering my question.

I know complex numbers are used to simplify calculations. I electronics, in quantumphysics and field theory and perhaps a lot of other branches as well.

If you in the equation m=m0/(1-sqrt(v^2/c^2)) set v=c then you divide by zero, thus, velocities with mass at the speed of light is forbidden. But if you set v .gt. c you get a imaginary component for the mass. The equation doesn't forbid velocities faster than light but the phycisists cannot interpret mass with a imaginary component.

We haven't seen anything in nature with a complex number yet, but is it possible to have for instance a mass with a imaginary component? Is it provable that it is impossible? Or is it possible, not yet provable? Then, perhaps faster than light velocities really is possible?

My teacher in physics says it is impossible, but he doesn't know why. On the other hand he thinks that dual time dimensions is impossible also, and not knowing why.
4. 28 Oct '07 18:062 edits
Originally posted by TheMaster37
In quantummechanics it helps reduce the amount of calculating to be done.

Complex exponents are way easier to deal with than a bunch of sines and cosines.
Also, sines and cosines are, essentially, i's and e's.

sinx=[e^(ix)-e^(-ix)]/2i, etc.

I believe that the work of vectors can be, and originally were, done using i, j and k (that is, the complex numbers over 4 dimensions).

EDIT: 4 dimensions, not 3.
5. 28 Oct '07 18:13
Originally posted by genius
I believe that the work of vectors can be, and originally were, done using i, j and k. That is, the complex numbers over 3 dimensions.
No.This is just a notation to indicate to indicate the unit vectors aling the three axes. It has nothing to do with complex numbers. Some people use î, ^j and ^k to denote the unit vectors and others use ^x,^y,^z but that's all that is to it.
6. 28 Oct '07 18:21
No.This is just a notation to indicate to indicate the unit vectors aling the three axes. It has nothing to do with complex numbers. Some people use î, ^j and ^k to denote the unit vectors and others use ^x,^y,^z but that's all that is to it.
http://en.wikipedia.org/wiki/Quaternion
7. 28 Oct '07 18:35
Originally posted by FabianFnas
I know complex numbers are used to simplify calculations. I electronics, in quantumphysics and field theory and perhaps a lot of other branches as well.

If you in the equation m=m0/(1-sqrt(v^2/c^2)) set v=c then you divide by zero, thus, velocities with mass at the speed of light is forbidden. But if you set v .gt. c you get a imaginary component for t ...[text shortened]... n the other hand he thinks that dual time dimensions is impossible also, and not knowing why.
In QM complex numbers arew more than just quickie ways to do the math. They are essential to it.

As for the other question we have no answer as fpor right now. I think that some experiments were done to see if tachyons could be detected and I know that they are used in many theories but experimental facst we have none.

Special relativity just says that if body starts we v
8. 28 Oct '07 18:45
Originally posted by genius
http://en.wikipedia.org/wiki/Quaternion
Are you talking about this?: the vector form of a quaternion may also be used. This form assumes that \vec{A} \equiv A_x\mathbf i + A_y\mathbf j + A_z\mathbf k. in that case the i,j,k are a notation to indicate the three coordinate axes and to explain how quaternions can be represented in that way. But don't you confuse a representation of an object with the object itself. Mathematical objects can have very representations.

But I think that if you read the informal introduction, and bare in mind the word informal, you can see that.
9. 29 Oct '07 00:08
Gracious sakes alive gentlemen....Granny is getting the vapors just listening to all this math lingo. Could anyone please explain it to Granny, in simple English... Is there a sq. root of minus 1 or not, and what is the simple answer ?

Granny
10. 29 Oct '07 03:47
Originally posted by smw6869
Gracious sakes alive gentlemen....Granny is getting the vapors just listening to all this math lingo. Could anyone please explain it to Granny, in simple English... Is there a sq. root of minus 1 or not, and what is the simple answer ?

Granny
Yes.
11. 29 Oct '07 04:01
Originally posted by AThousandYoung
Yes.
Dear god, you have left Granny hanging. Please, what IS the sq. root of minus one? Granny will promote you to 10^4 for the answer.

Granny.
12. 29 Oct '07 04:47
Originally posted by smw6869
Dear god, you have left Granny hanging. Please, what IS the sq. root of minus one? Granny will promote you to 10^4 for the answer.

Granny.
i
13. 29 Oct '07 15:14
Originally posted by AThousandYoung
i
i ???....So YOU are the sq root of minus one?

Granny.
14. 29 Oct '07 17:45
Originally posted by smw6869
i ???....So YOU are the sq root of minus one?

Granny.
Don't be such a square.
15. 29 Oct '07 21:03
Originally posted by Palynka
Don't be such a square.
So, i x i = -1 ?

Now it all makes sense!

G.