Dorky Poll: i or j?

Definitely i.

j is reserved for current density. I have known at least one engineer who admits this.

i

Aren't i, j and k all square roots of -1?

i

i, duh.

Doesn't it depend on context? If the question is about octonions, then i, j, k, and l are all correct.

i fear that this is a trick question, since i have NEVER come across anything other than "i"

But my fourth grade teacher said that only positive numbers have square roots!

script small "eye" is square root of minus one, or more usefully exp(2 * Pi * i) = 1. Most electron engineers have some outlandish idea that SS"E" is reserved for current and hence script small "jay" is square root of minus one. Given that electron engineers are occasionally useful in assuring that laboratory equipment functions properly or that electricity generating systems actually deliver current, such disrespect of proper tradition must be abided but under no condition either abetted or encouraged.
One must not lose sight that many of these individuals firmly hold that electrons, in the suitable classical limit, are inscribed with a "minus" sign and consider Cooper pairs to be some form of abomination.

i

(This is even a question?)

i! But interestingly, my electronics class (for physics majors) used j. I was devestated.

i; unless you are an engineer :)

Dude, it's 'i' because there's no 'j' in 'imaginary'.

i fear that this is a trick question, since i have NEVER come across anything other than "i"

"j" for sqrt(-1) showed up all the time in an introductory engineering course I took. Predictably, this led to snide references to "engjneers" and "engjneerjng".

Pi/2

I'm with # 3 (Rich): "Aren't i, j and k all square roots of -1?"

Quaternions, man. can't live without them. Used them on any number of Guidance, Navigation, and Control projects for rockets, missiles, spacecraft, and jet fighters.

i^2 = j^2 = k^2 = ijk = -1.

After quaternions, you can never go back to mere complex numbers.

http://mathworld.wolfram.com/Quaternion.html

And who's to say that the mass or charge of an elementary particle or string is not a quaternion? Or something beyond that, like octonions, or grassmannians, or something?

One should not discriminate against k: it's the funniest letter. Keokuk! Cucamonga!

j

i is the number of electrons (well charges) per second. Physics would be a lot different if you were using a constant value for that little guy. Much less an imaginary one.

i or j, it doesn't matter so much when what's important is the charge number density mixed with other fundamental units to get concentrations, or fluxes, or fluences, or etc. Plus, stuart, electrons per second doing what? Coulombs per second (i.e., the capital letter I) just isn't all that interesting without more information, e.g., number of high-energy electrons impacting on a satellite and potentially damaging equipment, number of electrons hopping onto a quantum dot and forming a Coulomb blockade, etc.

Now, if you're talking about waves propagation, there's no more room to futz around, no arguing over numbers of charges and related quantities. Hell, not even necessarily working with axes set in Euclidean geometry (hello, Mr. Ray Equations, hello Mr. Magnetic Field). The quantity is clearly then i, and for consistency should always be so labeled.

But most fundamentally, it's just notation. Define it clearly so that the people you are talking to have a clue. Thus j for engineers and i for people who have a clue about notation.

i

I am for i

Aye, i.

k, the unloved of the square roots of -1

i

AND I'm an engineer... plus I think I could take you, so no trying to toss ME out! :-P

the root of -1 is clearly jimaginary. j it is.

i, of course.

But, when it comes time to do AC circuits, I always do a bit of "pre teaching" to prepare them for engine school.

I tell them that physics puts its emphasis on the current density (always j) "at a more advanced level" and uses the DC current symbol I for most currents and the mathematical symbol i for sqrt(-1). Engineering puts its emphasis on the AC current symbol i, so they switched j to be the sqrt(-1) because they rarely deal with the current density.

I also explain a useful memory trick for the engineering choice: Everyone uses the i,j,k unit vectors. Notice that the "j" unit vector points along the "y" axis, which just happens to be where we put the imaginary axis for complex numbers. Coincidence? I don't know, but it is a great teaching tool.

Oh, and I tell them that if you know what you are doing you can use i for everything. The only person confused by i = i_max e^{i omega t} is the reader, not the writer.

i!

I may be an engineer, but if so, dammit, I'm a software engineer.

(Although really, the real answer a CS/software engineering person ought to be responding with here is that there's no such thing as i or j, there's just the 2-tuple [0,1].)

This is a trick question. There is no such thing as "the square root of -1". Even if you restrict yourself to C, -1 has two square roots (i and -i). And in the quaternions, for any purely imaginary quaternion q such that |q| = 1, eq is a square root of -1.
Most importantly, there is no field of characteristic 0 where -1 has a principal square root, which is what most people mean by "the square root".

This is a trick question. There is no such thing as "the square root of -1". Even if you restrict yourself to C, -1 has two square roots (i and -i). And in the quaternions, for any purely imaginary quaternion q such that |q| = 1, eq is a square root of -1.
Most importantly, there is no field of characteristic 0 where -1 has a principal square root, which is what most people mean by "the square root".

i for "imaginary", of course.

(If it were in my power to do so, I would honour that mathematician of the fanciful imagination, Mr C. Dodgson, and call it "Carroll's Number").

I prefer i but I try to teach my students (high school) to get used to see different symbols for most concepts and quantities. Think about how many symbols you can think of to represent energy depending of what context you use it. When it comes to imaginary number they need to be used to both i and j without any problem.

And to comment whoever said -i is a square root of -1 is wrong.

x=-i is a solution to x^2=-1 but that doesn't mean sqrt(-1)=-i no more then x^2=4 solution x=-2 means that sqrt(4)=-2

Although I suspect this is some kind of trick question (i, j and k are all used frequently in matrix representation as well), the correct answer is i, at least as I've learned it.

"This is a trick question. There is no such thing as "the square root of -1". Even if you restrict yourself to C, -1 has two square roots (i and -i). And in the quaternions, for any purely imaginary quaternion q such that |q| = 1, eq is a square root of -1."

I thought that i was principally a construct for a number that, when squared, was equal to -1. For my understanding the complex field was just an extension of the reals with a construct i that allowed you to work with negative roots. But granted I'm more pedestrian than your average pure/theoretical mathematician.

There is no "right and proper" choice (but of course - I'm both EE and PhD in E), but i is preferable where you can chose for reasons CCPhysicist sums up.

And Eulers identity is so much cooler when sounded out "raised to i pi".

It's not jmaginary ...

Tyler: That's correct. But the important point is that i (or j) is a square root of -1. It is not the square root of -1.

I would prefer that "i" represent "invisible" rather than imaginary.

Caspar Wessel proved this in 1797.

Charles Steinmetz associated "i" with electromagnetism using his IEEE phasor equations in the 1890s.

Both Wessel and Steinmetz should be acknowledged with a posthumous Gauss Prize or equivalent honor.

Leibniz (or whoever) created a serious misnomer using imaginary.

Kudos to those recognizing "j" and "k".

Doug, good point about the misnomer. I've had math faculty ask me if "imaginary numbers" are ever used for anything real in physics, wondering if they could just skip that part of the trig book where they do complex numbers! The narrowness of education ....

And Doug, could you post a good source about the origins of phasors by Steinmetz? I'd like to read about that.

i

"i! But interestingly, my electronics class (for physics majors) used j. I was devestated."

Mine too. Did you take 111-BSC at Berkeley?

"Dude, it's 'i' because there's no 'j' in 'imaginary'."

There is in "imajinary".

Imaginary numbers are tools of the devil.

Hi CCPhysicist,

I do not have direct access to IEEE which is probably the best source of information.

Maybe the next best place to start is with a Wiki biography and introduction.

Charles Proteus Steinmetz [200 patents as GE chief EE]
- other links and readings
http://en.wikipedia.org/wiki/Charles_Proteus_Steinmetz

Phasor (electronics) [a type of Grassmann Algebra]
http://en.wikipedia.org/wiki/Phasor_(electronics)

Also:

Charles Proteus Steinmetz [incredible-people]
"Thomas Edison founded the General Electric Company in 1886 and wanted to hire Steinmetz."
"Among Steinmetz's distinguished visitors was Marchese Guglielmo Marconi, inventor of the first practical radio system and recipient of the Nobel Prize for Physics in 1909.
Another of Steinmetz's distinguished visitors was Albert Einstein who came to Schenectedy in 1921. It was in that year Einstein received the Nobel Prize in physics. "
"Charles Proteus Steinmetz was "the most widely known professor ever a member of the Union College faculty." From 1902 to 1913 Steinmetz headed the School of Electrical Engineering and guided it in becoming one of the best in the nation."
"The IEEE Charles Proteus Steinmetz Award was established by the Board of Directors in 1979. It may be presented annually to an individual for major contributions to the development of standards in the field of electrical and electronics engineering. "
http://profiles.incredible-people.com/charles-proteus-steinmetz/

Eric Weisstein ScienceWorld.com, concise with links
Steinmetz, Charles Proteus (1865-1923)
http://scienceworld.wolfram.com/biography/Steinmetz.html

Many other Google sites listed. I could not find the one I first used about 5 years ago.

David Hestenes [ASU emeritus] explores relation of Grassmann and Clifford Algebras.
1 - The Kinematic Origin of Complex Wave Functions
2 - Clifford Algebra and the Interpretation of Quantum Mechanics
3 - Grassmann'sVision in Hermann Gunther Grassmann (1809-1877): Visionary Mathematician, Scientist and Neohumanist Scholar
http://modelingnts.la.asu.edu/

Another GE EE, Gabriel Kron, Electrical Circuit Models of the Schrodinger Equation,
Phys. Rev. 67, 39-43 (1945), also discusses transformation to mechanical models.
http://www.quantum-chemistry-history.com/Kron_Dat/Kron-1945/Kron-PR-194…

Like post #35, I propose it would be a solution to make it depend on your choice of direction of integration. Standard "i" for me, "j" if you choose oppositely. Thanks to Prof Christian Parigger at UT Space Institute for insight.