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[-] mariusafa@lemmy.sdf.org 5 points 1 day ago

What if not a Hilbert space?

[-] captainlezbian@lemmy.world 30 points 1 day ago

It’s just dimensionally shifted. This is not only true, its truth is practical for electrical engineering purposes. Real and imaginary cartesians yay!

[-] blackbrook@mander.xyz 44 points 1 day ago

You need to add some disclaimer to this diagram like "not to scale"...

[-] hydroptic@sopuli.xyz 54 points 1 day ago

It's to scale.

Which scale is left as an exercise to the reader.

[-] jerkface@lemmy.ca 8 points 1 day ago

I really don't think it is.

[-] hydroptic@sopuli.xyz 5 points 1 day ago

I may not have been entirely serious

[-] captainlezbian@lemmy.world 13 points 1 day ago

Yeah, 1 and i should be the same size. It’s 1 in the real dimension and 1 in the imaginary dimension creating a 0 but anywhere you see this outside pure math it’s probably a sinusoid

[-] puchaczyk@lemmy.blahaj.zone 41 points 1 day ago

This is why a length of a vector on a complex plane is |z|=√(z×z). z is a complex conjugate of z.

[-] randy@lemmy.ca 18 points 1 day ago

I've noticed that, if an equation calls for a number squared, they usually really mean a number multiplied by its complex conjugate.

[-] drbluefall@toast.ooo 6 points 1 day ago

[ you may want to escape the characters in your comment... ]

[-] kryptonianCodeMonkey@lemmy.world 45 points 2 days ago

Imaginary numbers always feel wrong

[-] bitcrafter@programming.dev 7 points 1 day ago

If you are comfortable with negative numbers, then you are already comfortable with the idea that a number can be tagged with an extra bit of information that represents a rotation. Complex numbers just generalize the choices available to you from 0 degrees and 180 degrees to arbitrary angles.

[-] Klear@lemmy.world 19 points 1 day ago

After delving into quaternions, complex numbers feel simple and intuitive.

[-] affiliate@lemmy.world 17 points 1 day ago

after you spend enough time with complex numbers, the real numbers start to feel wrong

[-] TeddE@lemmy.world 5 points 1 day ago

Can we all at least agree that counting numbers are a joke? Sometimes they start at zero … sometimes they start at one …

[-] ___qwertz___@feddit.org 1 points 7 hours ago

ISO 80000-2 defines 0 as a natural number. qed.

[-] Enkers@sh.itjust.works 28 points 2 days ago

I never really appreciated them until watching a bunch of 3blue1brown videos. I really wish those had been available when I was still in HS.

[-] driving_crooner@lemmy.eco.br 22 points 1 day ago* (last edited 1 day ago)

After watching a lot of Numberphile and 3B1B videos I said to myself, you know what, I'm going back to college to get a maths degree. I switched at last moment to actuarial sciences when applying, because it's looked like a good professional move and was the best decision on my life.

[-] jerkface@lemmy.ca 14 points 1 day ago* (last edited 1 day ago)

Doesn't this also imply that i == 1 because CB has zero length, forcing AC and AB to be coincident? That sounds like a disproving contradiction to me.

[-] xor@lemmy.blahaj.zone 7 points 1 day ago

I think BAC is supposed to be defined as a right-angle, so that AB²+AC²=CB²

=> AB+1²=0²

=> AB = √-1

=> AB = i

[-] jerkface@lemmy.ca 2 points 19 hours ago

I mean, I see that's how they would have had to get to i, but it's not a right triangle.

[-] Knock_Knock_Lemmy_In@lemmy.world 1 points 7 hours ago

i is at a right angle (pi/2) to 1 by definition.

[-] BorgDrone@lemmy.one 18 points 1 day ago
[-] Rivalarrival@lemmy.today 15 points 1 day ago

That's actually pretty easy. With CB being 0, C and B are the same point. Angle A, then, is 0, and the other two angles are undefined.

[-] crmsnbleyd@sopuli.xyz 2 points 1 day ago

A is clearly a right angle

[-] Rivalarrival@lemmy.today 3 points 1 day ago

A is drawn in such a way that it resembles a right angle, but it is not labeled as such. The length of the hypotenuse is given as zero. The opposite angle cannot be anything but 0°.

[-] crmsnbleyd@sopuli.xyz 6 points 1 day ago

The pythagoras theorem only holds if A is a right triangle

[-] Rivalarrival@lemmy.today 1 points 19 hours ago

What is depicted here isn't even a polygon, let alone a triangle, let alone a right triangle. This is just a line segment. Line AB is the same as line AC. There is no line BC. BC is a single point.

I suppose it could possibly depict a weird cross section of two orthogonal circles in a real and an imaginary plane.

[-] hydroptic@sopuli.xyz 5 points 1 day ago

No thank you

[-] ornery_chemist@mander.xyz 35 points 2 days ago

Isn't the squaring actually multiplication by the complex conjugate when working in the complex plane? i.e., √((1 - 0 i) (1 + 0 i) + (0 - i) (0 + i)) = √(1 + - i^2^) = √(1 + 1) = √2. I could be totally off base here and could be confusing with something else...

[-] HexesofVexes@lemmy.world 1 points 7 hours ago* (last edited 7 hours ago)

Almost:

Lengths are usually reals, and in this case the diagram suggests we can assume that A is the origin wlog (and the sides are badly drawn vectors without a direction)

Next we convert the vectors into lengths using the abs function (root of conjugate multiplication). This gives us lengths of 1 for both.

Finally, we can just use a Euclidean metric to get our other length √2.

Squaring isn't multiplication by complex conjugate, that's just mapping a vector to a scalar (the complex | x | function).

[-] diaphanous@feddit.org 16 points 1 day ago

I think you're thinking of taking the absolute value squared, |z|^2 = z z*

[-] candybrie@lemmy.world 6 points 1 day ago

Considering we're trying to find lengths, shouldn't we be doing absolute value squared?

[-] owenfromcanada@lemmy.world 27 points 2 days ago

This is pretty much the basis behind all math around electromagnetics (and probably other areas).

[-] A_Union_of_Kobolds@lemmy.world 14 points 2 days ago

Would you explain how, for a simpleton?

[-] L0rdMathias@sh.itjust.works 23 points 1 day ago

Circles are good at math, but what to do if you not have circle shape? Easy, redefine problem until you have numbers that look like the numbers the circle shape uses. Now we can use circle math on and solve problems about non-circles!

[-] owenfromcanada@lemmy.world 31 points 2 days ago

The short version is: we use some weird abstractions (i.e., ways of representing complex things) to do math and make sense of things.

The longer version:

Electromagnetic signals are how we transmit data wirelessly. Everything from radio, to wifi, to xrays, to visible light are all made up of electromagnetic signals.

Electromagnetic waves are made up of two components: the electrical part, and the magnetic part. We model them mathematically by multiplying one part (the magnetic part, I think) by the constant i, which is defined as sqrt(-1). These are called "complex numbers", which means there is a "real" part and a "complex" (or "imaginary") part. They are often modeled as the diagram OP posted, in that they operate at "right angles" to each other, and this makes a lot of the math make sense. In reality, the way the waves propegate through the air doesn't look like that exactly, but it's how we do the math.

It's a bit like reading a description of a place, rather than seeing a photograph. Both can give you a mental image that approximates the real thing, but the description is more "abstract" in that the words themselves (i.e., squiggles on a page) don't resemble the real thing.

[-] ggtdbz@lemmy.dbzer0.com 2 points 18 hours ago

I remember the first time we jumped into the complex domain in an electronics course to calculate something that we couldn’t reach with the equations we had so far.

… and then popping out the other side with a simple (and experimentally verified) scalar, after performing some calculation in the complex domain, using, bafflingly, real world inputs.

I suddenly felt like someone from the future barged into my Plato’s cave and proceeded to perform some ritual.

Like I know what’s happening, I’ve done these calculations before, but seeing them used as an intermediate step in something real in the real world was pretty cool!

Did not prepare me for all the Laplace et al shenanigans later. Did I test well in those courses? No. Did I have the most fun building the circuits regardless? You bet.

Oh to be a student again. Why are real world jobs so boring.

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[-] ShinkanTrain@lemmy.ml 13 points 1 day ago
[-] produnis@discuss.tchncs.de 13 points 1 day ago

Too complexe for me ;)

[-] iAvicenna@lemmy.world 11 points 1 day ago

you are imagining things

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this post was submitted on 30 Oct 2024
385 points (97.3% liked)

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