The Official "Quick Question" Thread

[Asterisk Propernoun]

So, I'm having problems with understanding imaginary units. My friend told me that -i=i, but I confused him when I showed him this:

 

-i=i

2i=i+i=i+(-i)=i-i

i-i=2i?

 

I must be missing something...

[Acme]

So, I'm having problems with understanding imaginary units. My friend told me that -i=i, but I confused him when I showed him this:

 

-i=i

2i=i+i=i+(-i)=i-i

i-i=2i?

 

I must be missing something...

You misunderstood. i equals the square root of negative one.

[math]i=\sqrt{-1}[/math]

or

[math]i^2=-1[/math]

[Asterisk Propernoun]

You misunderstood. i equals the square root of negative one.

[math]i=\sqrt{-1}[/math]

or

[math]i^2=-1[/math]

 

That much I get, but I was told that, since i is solely defined by i²=-1, that there's no difference between i and -i because you can square the negative version of a number and get the same answer:

 

2²=4=(-2²)

Edited August 27, 2014 by Asterisk Propernoun

[Acme]

That much I get, but I was told that, since i is solely defined by i²=-1, that there's no difference between i and -i because you can square the negative version of a number and get the same answer:

 

2²=4=(-2²)

You wrote

2i=i+i=i+(-i)=i-i

You can't simply make the substitution of (-i) for one of the i's from the 2i midstream. Both of the i's from the 2i are positive.

 

If you have a specific problem using i in an equation or expression with some utility, then by all means present it.

[Strange]

 

That much I get, but I was told that, since i is solely defined by i²=-1, that there's no difference between i and -i because you can square the negative version of a number and get the same answer:

 

By that logic, there is no difference between 10 and -10. Try telling that to your bank next time you go overdrawn!

[Endy0816]

 

That much I get, but I was told that, since i is solely defined by i²=-1, that there's no difference between i and -i because you can square the negative version of a number and get the same answer:

 

Square roots have both positive and negative results.

 

[latex]\pm \sqrt 4 = (2,-2)[/latex]

 

So 2 squared equals 4, but taking the square root of 4 yields both positive and negative 2. So you can't end up in a logic breakdown where 2 = -2(or anything similar).

Edited August 28, 2014 by Endy0816

[Asterisk Propernoun]

 

Square roots have both positive and negative results.

 

[latex]\pm \sqrt 4 = (2,-2)[/latex]

 

So 2 squared equals 4, but taking the square root of 4 yields both positive and negative 2. So you can't end up in a logic breakdown where 2 = -2(or anything similar).

You wrote

You can't simply make the substitution of (-i) for one of the i's from the 2i midstream. Both of the i's from the 2i are positive.

 

If you have a specific problem using i in an equation or expression with some utility, then by all means present it.

 

By that logic, there is no difference between 10 and -10. Try telling that to your bank next time you go overdrawn!

 

I think you all are misunderstanding what I'm trying to say:

 

I am not trying to say that -2=2, because 2 isn't soley defined as being the solution to a²=4.

 

However, my friend from the other day told me that i is soley defined by i²=-1, meaning that -i=i because they're both solutions to a²=-1, and this is confusing me because, like I've shown, that would mean you could substitute i with -i when adding i and i together, thus turning it into i minus i without changing the end result, which is 2i.

 

The problem I'm having is understanding how i is defined. Was my friend wrong in saying that the only thing that defines i is i²=-1? Was he right about that, yet wrong when he said that this leads to i=-i? Was I wrong when I said that this opens up the possibility for i-i=2i? I honestly don't know. I'm confused.

 

EDIT: At Acme. I'm not trying to solve any specific equations. For now, I'm just trying to understand and get used to the concept.

Edited August 30, 2014 by Asterisk Propernoun

[ajb]

... this leads to i=-i?

 

This is not true.

 

What is true is that [math]i^{2} = (-i)^{2}= -1[/math]. Meaning that you could also define [math]k = \sqrt{-1}[/math] where [math]k=-i[/math]. That much is okay, you can "rotate" i to -i and the defining property does not change.

Edited August 30, 2014 by ajb

[Asterisk Propernoun]

you can "rotate" i to -i and the defining property does not change.

 

So what you're saying is that I can rotate the complex plane 180^o along it's real axis and make it to where -i is on top and i is on the bottom without consequence? This would make sense to me, seeing as it wouldn't lead to -i=i since, not only would it make positives into negatives, but it would also at the same time make negatives into positives, thus maintaining a difference.

Edited August 30, 2014 by Asterisk Propernoun

[ajb]

So what you're saying is that I can rotate the complex plane 180^o along it's real axis and make it to where -i is on top and i is on the bottom without consequence?

Such a rotation will have no consequences as far as the choice of i and -i as the imaginary unit. Which is really where the confusion about i and -i has come from.

 

 

This would make sense to me, seeing as it wouldn't lead to -i=i since, not only would it make positives into negatives, but it would also at the same time make negatives into positives, thus maintaining a difference.

Exactly, there is no fundamental difference in picking i or -i as your starting place for defining complex numbers.

[Asterisk Propernoun]

Such a rotation will have no consequences as far as the choice of i and -i as the imaginary unit. Which is really where the confusion about i and -i has come from.

 

 

 

Exactly, there is no fundamental difference in picking i or -i as your starting place for defining complex numbers.

 

Okay, I see. Thank you for telling me.

[random_soldier1337]

Sort of quick question, though more engineering than pure science. What is the effect of applying a DSB-SC modulated waveform to a non-coherent/asynchronous demodulator/detector such as an envelope detector or rectifier detector and why would we see such an effect?

 

I tried google for this but I just get explanations for the detectors themselves rather than this particular effect.

[Cryptid]

Quick Question: Is there a such type of science known as...or about the mysteries of the world? Like unexplained mysteries, paranormal, creatures, aliens, etc.? I mean, I know aliens involved space and stuff like that, but is that still some kind of science?

[Phi for All]

Quick Question: Is there a such type of science known as...or about the mysteries of the world? Like unexplained mysteries, paranormal, creatures, aliens, etc.? I mean, I know aliens involved space and stuff like that, but is that still some kind of science?

 

"Unexplained", in this context, means things for which the natural explanation is ignored in favor of an "unexplained" supernatural reason. It's not science, it's not evidence-based.

 

Pseudo-science, maybe? "Paranormal" is just "supernatural" in a fright wig.

[swansont]

Quick Question: Is there a such type of science known as...or about the mysteries of the world? Like unexplained mysteries, paranormal, creatures, aliens, etc.? I mean, I know aliens involved space and stuff like that, but is that still some kind of science?

It seems to me that most unexplained phenomena are ones for which insufficient evidence exist. If you don't have evidence to examine, you don't have science. Evidence is sometimes sparse if these are rare events.

[ajb]

Quick Question: Is there a such type of science known as...or about the mysteries of the world?

All science research is about understanding the mysteries of the world. Science is really a philosophy or general methodology that is used in understadning the world. The key concept is objective evidence.

 

Like unexplained mysteries, paranormal, creatures, aliens, etc.? I mean, I know aliens involved space and stuff like that, but is that still some kind of science?

You can approach all these subjects scientifically. If you do so then very little of the 'paranormal' really remains: there is just not the evidence to support any of the general claims here.

 

As for creatures, sometimes animals that are thought to be extinct or just just myths have been found: wikipedia will give you some nice examples. The general study of mythical creatures is known as cryptozoology and is usually considered pseudoscience. Not many people who study things like bigfoot follow the scientific method, for example.

 

The same can be said of aliens as far as UFOlogy is conserned. Not many 'believers' follow the scientific method. This is not the same as astrobiology, which is a science.

[EdEarl]

Has anyone written speculations of interuniversal space of the multiverse, other than string theory branes?

[ajb]

Has anyone written speculations of interuniversal space of the multiverse, other than string theory branes?

There are various brane cosmologies, for instance the Randall–Sundrum models. You could have a look at

 

Roy Maartens and Kazuya Koyama, Brane-World Gravity, Living Rev. Relativity 13 (2010), 5.

[TheMadWriter]

I'm not sure I'm doing this right (new here!) but I have my own quick question. Anyway, can dogs pinpoint exact barometric pressure changes. I know they can tell when it changes overall, because thats how they know about storms, but can they "sense" the exact point? Sorry, this might be too long.

Thanks!

[Sriman Dutta]

No, I think !!

[Danijel Gorupec]

Cannot find English term... In my language there is a very specific term for a point or area where a force is acting upon. A force has direction, magnitude and this-thing-that-is-its-origin-point. A direct translation by google translate tool returns the word "vertex" but I don't know if this is it... Anybody knows what I am talking about?

[Danijel Gorupec]

I am afraid I have another quick question... I remember that long time ago I read that a very small grain of iron might spontaneously become magnetic (will exhibit external magnetic field). Is this true, and does this effect have a specific name? The effect seems logical to me, but I cannot find anything about it - possibly because I don't know search terms.

[Lord Antares]

I think there is a bit of a contradiction in your question. Is it a point where it is acting upon or a point where it is originating from? Because these are two different things. Maybe you meant to say a point where it is acting FROM?

Anyway, assuming you're from the Balkans, can you give the term in the original language?

[Danijel Gorupec]

I think there is a bit of a contradiction in your question. Is it a point where it is acting upon or a point where it is originating from? Because these are two different things. Maybe you meant to say a point where it is acting FROM?

 

Anyway, assuming you're from the Balkans, can you give the term in the original language?

Yes, I think "is acting from" could be better description. In my language we call it 'hvatiste' (with an inverted hat over 's').

[Lord Antares]

I know there's a ''š'' over the word. We speak the same language.

Hmm, it's really strange. I googled the term ''vertex'' and it really isn't the same as ''hvatište''. There is only one website that attempts to translate the word, and it is into: ''point of application of a force''. That doesn't sound right. Doesn't sound like a term.

Anyway, googling further, I think there is no word for it really. I think English uses different words for different uses of the word ''hvatište''.
For example, take this text: ''U fizici, točka tijela u kojoj djeluje sila. Primjerice, hvatište sile teže u težištu je tijela, hvatište težine u ovjesištu ili uporištu, a hvatište je uzgona u geometrijskom središtu uronjenoga dijela tijela.''

That would suggest that, talking about gravity, hvatište is simply the center of mass.

Other forms of force would require different terms in English, I guess.