/sci/ - Science & Math

>>10053522
there is no one basic unit of any complex number. complex numbers are inherently 2 dimensional relative to the reals and as such every complex number is uniquely determined by a real value and an imaginary value.
i'd say that it would be valid to consider "1 and i" to be the two basic units of any complex number.
Though you haven't defined "basic unit," which clearly indicates that you don't have the background to have this conversation. I defined it as a basis element, you might mean a generator of the algebra over R. I'm not really sure what you're trying to get at.

i is the imaginary number which would occur should there be a principal square root of negative one, yes. -i could occur if instead we considered a different branch of the square root. so i'd argue that there's nothing fundamental about i (and it's a well known fact that complex conjugation is one of the particularly nice field automorphisms of C)

i is not a negative number, so just because i*i = -1 doesn't mean that there is a negative number which when multiplied by another negative number produces a negative number. I'll remind you what I said before, there's no way to nicely define an order on a field like C, so unless you want to talk about 1 dimensional subspaces on C and orders on those (which would be meaningless in this situation) your idea of "negative numbers multiplying to negatives" is woefully ill defined.

the fourth quadrant? they name those in middle school, right? no mathematician ever calls it Quadrant IV, or ever refers to quadrants of R^2. in the complex plane, this consists of complex numbers with positive real part and negative imaginary part - not seeing how it relates you your point, since the product of any two such numbers stays in the lower half plane. no product of these will ever be negative (i.e. hit the negative real axis) under a reasonable definition of negative.

you also use the term "series," and yet i notice no sequence of partial sums

Real Analysis I (4)
Abstract Algebra I (4) (this is just group/ring/field theory for babies afaik)
Comparative Literature 1A (4) - Crime in Literature (le meme breadth requirements)
General Chemistry 1 (3)
General Chemistry 1 Lab (1)

tfw freshman in upper division math classes
hey, at least we're using baby rudin and fraleigh, which should both be pretty fun.

>>9202786
:^) you're joking, right friendo?

I started on a whim a week ago, this is my first semester.
It was a great decision. All my psets look nice and pretty and it was really quick to learn most of the symbols I typically need.
I'm getting closer to wanting to just take notes in it, but I'm not sure. Can't use a laptop in most of my lectures regardless. Doing homework in it is good enough for now.