My point is that the way that you stick two real numbers together to make a complex number is important, and is unintuitive if you approach it as just two real numbers.

I’m being combative because I don’t get how you don’t understand our argument, and because I view claims like “You keep claiming things that are objectively false” to be hostile when they stem from a misunderstanding rather than a fault on my part.

Let me restate my main point: complex numbers can be defined as vectors with the necessary rules to define various operations, such as multiplication over them and how they relate to sqrt(-1). Those additional rules are just as important to their definition as their appearance as two real-numbered values is. Both vectors and complex numbers are defined by humans, but we have chosen to give them separate definitions, because each definition includes the rules defining these operations and relationships, and they are different between the two types of mathematical object.

And, for the record, I downvoted your posts that were hostile (not all of them) and responded in kind. It’s a separate effort than trying to prove my point here.

Right, but you need to specify that additional definition. Imaginary numbers are useful because they come pre-loaded with all those additional definitions about how to handle operations that use them.

I also find your hostile confusion unwarranted, given two other commenters have pointed out the same flaw in your argument that I have.

Maybe the image is of an arched ibex?

I’m reading this after lemm.ee is gone

A math discovery unmotivated by research in other fields; just discovering math to see if it works out

I don’t think this is really an accurate way of thinking about them. Yes, they can be mapped to a 2d plane, so you can represent them with their two real-numbered coordinates along the real and imaginary axes, but certain operations with them (eg. multiplication) can be done easily with complex numbers but are not obvious how to carry out with just grid points. (3,4) * (5,6) isn’t well-defined, but (3+4i) * (5+6i) is.

Somewhat related fun fact: One of the most concrete applications for quantum computers so far is breaking some encryption algorithms.

Imaginary numbers probably, they’re useful for a lot of stuff in math and even physics (I’ve heard turbulent flow calculations can use them?) but they seem useless at first

I like to imagine I’m yelling it. SUDO!!!

sudo !!

Erm ackshually singular “they” is centuries old now

Me

Yup. Once you recover from a stall a few times you can get pretty fast at it, but don’t worry about going slow and methodical.

I do, but I don’t have a whole lot else going on

At least they usually show the real datetime on hover

I wouldn’t expect it to be the rounding; either it’s a material thing or they’re talking about colors that can’t be represented inside the RGB color space.

Steam is not better than discord lmao

RIP. Thanks for all you’ve done.