quote:Original post by sadwanmage
I dunno about the rest of the world, but here in England convention has recently changed so that j instead of i is the sqrt(-1), so both are used and everyone is confused. I had no idea other countries had a different convention.

Here (United States) i is typically (-1)1/2 (at least as far as I''ve pursued math), but recently in my abstract algebra course the professor introduced quaternions as an extension of the complex numbers. Which seems quite different from their interpretation here (gamedev.net, or any place dealing with animation). Yes, I realize they''re equivalent, but it''s somewhat on topic because i2=-1, j2=-1, and k2=-1, with other products (e.g. ik) being what you''d expect from the unit vectors i, j, and k (which are being replaced by the unit vectors x, y, and z in my courses at present. I miss i,j,k, but realize it''s probably for the best.)

MrScout, I believe the j you are referring to is something different. I vaguely remember reading about it in QED (an excellent book). It as a number very near unity as far as I recall, but I may have forgotten a factor of i. It was used in alculating the probability of an event happening. If two events happened in a Feynman diagram, you would use j2 and if there were 4 then a forth power etc. I cannot find anything on the internet on it with a quick search though...

You mean you guys have locally consistent (if varying) definitions for i and j?
In Australia, if you're a mathematician sqrt(-1) = i.
If you're an electrical engineer sqrt(-1) = j.
I guess if you're a C++ programmer sqrt(-1) = complex<double>(0, 1)

[edit: damn html]

[edited by - fractoid on February 28, 2004 8:42:06 AM]

quote:Original post by ToohrVyk
In France, we use "j" in mathematics as exp( i * 2 * pi / 3 ).
However, in physics, j is used instead of i, especially when working with alternative currents (so i is already used as a notation for the intensity of those currents).

Interesting, we use I for linear currents and J for volume currents. So I guess it''s a non-issue since using the capital letters prevents any ambiguity. However, beyond the general physics courses, we typically don''t use i, j, and k as our unit vectors any more because k as the wave vector has become more prominent.

quote:
Way Walker : given a complex number z, what is z^(1/2) ? There is no unique solution for x² = z equations over C (and not over R either). But unlike R, there''s no "positive root" discrimination available : there are two really distinct roots without an indiscutable way of separating the two of them.

I''m not sure I understand your complaint. Do you prefer i2=-1, i=(-1)1/2, or i=sqrt(-1) (where you''d replace sqrt with radical notation)? Heh, I study math and physics, so I''m typically too relaxed in my notation for mathematicians and too pedantic for physicists.

quote:
I might be wrong, but I don''t think that if you replaced in all your formulas i with (-i), you''d change a lot of things.

Hmm? It does change things, you''ve just taken the conjugate. For instance, if z is complex, z2 and z*z (where z* is the complex conjugate of z) are in general not the same thing.