Problem is: you have chosen an orientation (x rightwards, y upwards). That makes your choice of i/-i not canonical: as is natural, because it cannot be canonical.
It is an interesting question whether it would be possible to distinguish the 2 senses of rotation in a plane that is not embedded in a 3-dimensional space where right and left are easily distinguished. The answer seems to be no.
While in a plane, if you choose 2 orthogonal vectors, from that moment on you can distinguish clockwise from counterclockwise and -i from +i, based on the order of the 2 chosen vectors.
However, from the point of view of a 3-dimensional observer that would watch this choice, it will probably look random, i.e. the senses of rotation would either match those that the 3-dimensional observer thinks as correct, or be the opposite, and within the plane there would be no way to recognize what choice has been made.
This is no big deal. Similarly, in an affine plane there is no origin, but after you choose a particular point then you have an origin to which you can bind a vector space with a system of coordinates, where the senses of rotation are established after the choice of 2 non-collinear vectors.
In an affine plane, the choice of 1 point eliminates the symmetry of translation, then the choice of 1 vector eliminates the symmetry of rotation, and then the choice of a 2nd non-collinear vector eliminates the symmetry between the 2 senses of rotation, allowing the complete determination of a system of coordinates for the 2-dimensional vector space and also the complete determination of the associated field of complex numbers.
I was in a fraternity in college, 20 years ago. We put weekly bathroom notes on the inside of the stall doors. Something interesting, something funny, upcoming news. The elected fraternity secretary was responsible for making those weekly, among many other things.
If they were a day late the amount of pestering they would get until the did that weekly job was hilarious. We all got a kick out of them.
Your toilet time can be yours, just don’t fucking read them lol. Back then razr phones were the hotness, nobody sat on a smartphone and had ads blasted at them while they took a shit.
I guess, if you equate "influence" with "abuse". An awful lot pillars of our society would become abuse then. Ask any parent of a toddler whether their toilet time is actually "theirs".
My point is the opposite actually: if you are the parent of a toddler, you'll know that your toilet time is not actually yours, because your toddler will try every effort to get your attention and influence you, up to and including crawling into your lap while you are doing your business; tantrumming on the bathroom floor; tantrumming outside the bathroom door; cutting up the mail you really need to file; spilling food all over the floor; unlatching childproofing; moving furniture; and enlisting their siblings.
There is no way to distinguish between "i" and "-i" unless you choose a representation of C. That is what Galois Theory is about: can you distinguish the roots of a polynomial in a simple algebraic way?
For instance: if you forget the order in Q (which you can do without it stopping being a field), there is no algebraic (no order-dependent) way to distinguish between the two algebraic solutions of x^2 = 2. You can swap each other and you will not notice anything (again, assuming you "forget" the order structure).
Building off of this point, consider the polynomial x^4 + 2x^2 + 2. Over the rationals Q, this is an irreducible polynomial. There is no way to distinguish the roots from each other. There is also no way to distinguish any pair of roots from any other pair.
But over the reals R, this polynomial is not irreducible. There we find that some pairs of roots have the same real value, and others don't. This leads to the idea of a "complex conjugate pair". And so some pairs of roots of the original polynomial are now different than other pairs.
That notion of a "complex conjugate pair of roots" is therefore not a purely algebraic concept. If you're trying to understand Galois theory, you have to forget about it. Because it will trip up your intuition and mislead you. But in other contexts that is a very meaningful and important idea.
And so we find that we don't just care about what concepts could be understood. We also care about what concepts we're currently choosing to ignore!
This is arguable for HSBC (in the UK at least). Ringfencing laws post 2008 have made customer deposits in the UK very difficult to invest profitably, to the point where (at least last time I cared about this) they were charging commercial customers to have UK domiciled accounts.
> Ringfencing laws post 2008 have made customer deposits in the UK very difficult to invest profitably, to the point where (at least last time I cared about this) they were charging commercial customers to have UK domiciled accounts.
I don't follow; why would regulations on consumer accounts change the price of commercial customer accounts?
Small businesses accounts were/are also subject to ring fencing, and my recollection is that large banks sought to recover the costs of ringfencing rules via charges on large clients.
Come to think of it this was all also at the time of very low rates which was more likely to be the issue.
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