Lmst

🎉 Ah yes, because every 8-year-old spends their weekends itching to dive into the exhilarating world of complex numbers 🤓. This book promises a "real-life journey"—because nothing screams "relatable" like imaginary units and polar coordinates 🙄.
https://mathwonder.org/Having-Fun-with-Complex-Numbers/ #complexnumbers #relatablelearning #mathhumor #educationalbooks #HackerNews #ngated

just in case anyone is interested in how to do complex linear algebra, including complex tensor products, without using complex numbers - using real linear operators $J$ with $J\circ J=-I$ instead of complex scalars - here are some links.

The TLDR version on a poster:
http://mwaa.math.indianapolis.iu.edu/Slides/coffman.pdf

Using a basis, matrices, and summing over indices - sections 4&5 of this paper:
https://users.pfw.edu/CoffmanA/pdf/basis1.pdf

Without a basis (but still a lot of notation) - Chapter 5 starting on page 195, with tensor products starting with Example 5.74 on page 208:
https://users.pfw.edu/CoffmanA/pdf/book.pdf
#LinearAlgebra #ComplexNumbers #NotASubToot

Explore infinite beauty with the mesmerizing Mandelbrot Set! https://www.funkysi1701.com/posts/2025/mandelbrot-set/ #mandelbrotset #fractals #mathematics #chaostheory #complexnumbers #art #visualization #mathart #self-similarity #complexdynamics

💥 Breaking news from the future: Quantum computers still can't factor the nail-bitingly complex number 21! 🙃 Apparently, it only took 24 years to realize that maybe the answer lies in some ancient figure from 2001. Math enthusiasts are SHOCKED! 🤯
https://algassert.com/post/2500 #QuantumComputing #MathNews #HackerNews #FutureTech #ComplexNumbers #Shocked #HackerNews #ngated

🔢➡️🤯 Oh look, someone thought it was a good idea to combine integer continued fractions with complex numbers. Because clearly, math wasn't complicated enough! 😂 Thanks, Cormac, for ensuring we have endless fun trying to solve puzzles nobody asked for. 🙄
https://arxiv.org/abs/2508.15078 #mathfun #integerfractions #complexnumbers #puzzlegames #CormacHackerNews #HackerNews #ngated

Prisms Math

** SUBSCRIPTION REQUIRED (US $23.99/year)**

- VR content modules for students to deepen their understanding of core concepts

#Fractions
#Ratios
#Rate_of_Change
#Probability
#Surface_Area

#Algebra
#Geometry
#Advanced Algebra
#ComplexNumbers
#PolarCoordinates
#VectorAddition
#Ellipses
#Matrices

https://www.meta.com/experiences/app/8875714305775804/?utm_source=oculus&utm_medium=share

Decagon (fractal version)

$z_{n+1}=fold(z_n)^2+c$

where fold is a generalized absolute value function. A complex number has two components: a real and an imaginary part.
If we take the absolute value of one of these parts, we can interpret this as a fold in the complex plane. For example, |re(z)| causes a fold of the complex plane around the imaginary axis, which means that the left half ends up on the right half. If we do this for the imaginary component |im(z)|, we fold the complex plane around the real axis which means that the bottom half ends up on the top half.
These two operations are quite similar, because the imaginary fold is just like the real fold of the plane, except that it was previously rotated 90 degrees (z * i). But what if we rotate the plane by an arbitrary number of degrees?
An arbitrary rotation of the complex plane can be expressed as rot(z, radians) = z * (cos(radians) + sin(radians) * i), where radians encodes the rotation.

The image here is produced, by rotating the plane exactly five times, and folding the imaginary part each time.

I found this algorithm in the Fractal Formus under the name “Correction for the Infinite Burning Ship Fractal Algorithm”.
It can be seen as a generalization of the burning ship obtained by folding the complex plane twice with a rotation of 90 degrees, i.e. folding both the real and the imaginary part.

#fractalfriday #fractal #burningship #mandelbrot #complexplane #complexnumbers #mathart #math #escapetimefractals

$Black fractal structures on a mostly green background, rendered using distance estimation.$

Some relationships just don’t add up.
But in math? It’s all about real and imaginary compatibility.

🔗 https://techgeeksapparel.com/its-complex-funny-math-t-shirt/
#MathRomance #ComplexNumbers #AlgebraLove #NerdLife

Is Nature complex or hypercomplex?
#quantumphysics #quantummechanics #complexnumbers #research #science
🤓

https://phys.org/news/2025-03-quantum-mechanics-hypercomplex-complex.html

#mathartmarch II: On a square grid

A third degree Newton fractal zoom in.

Domain coloring technique adapted from this beauty: https://www.shadertoy.com/view/wld3zl
Sorry for the not-so-high quality, I'm too lazy to export it to a direct video at the moment.

#grid #newton #fractal #complexnumbers #complexplane #glsl #shader

What are the #mathematics behind this animation?

https://youtu.be/KlNOszFY3GI

#mathart #geometry #recursion #complexnumbers

@bytebro

#PreshTalwalkar did this one a year ago, and without much shouting to boot. (-:

https://youtube.com/watch?v=R476CTKUIr4

#ComplexNumbers #logarithms #maths #fallacies

Every polynomial with real coefficients factors into linear and quadratic terms.

How much machinery is needed to show this?

If it crosses the X-axis then it has a linear term.

If it doesn't cross the X-axis then it is of even degree, and the roots come in complex conjugate pairs.

What the minimum needed to see this?

#maths #math
#algebra #ComplexNumbers
#MathsChat #MathChat

Faffing about with complex numbers again

Integers have these things called complex conjugates. This is something I have just been learning about. Or not. You’ll soon see my mathematical shortcomings. This thing is, I think, a way to express them as complex numbers. (I think that was the takeaway of the videos I just watched).

I’d better quote the wiki because that feels like a rubbish explanation:

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.
Complex conjugate, Wikipedia

The first five look like this according to Google’s AI

IntergerComplex conjugate1122-0i33-i4455

I’m only actually interested in the first three because we could do something fun with those.

I previously showed my broken work as I wondered about the Collatz Conjecture over the complex plane. Mostly I wanted to know if complex numbers could be odd or even.

It’s possible to define even and odd Gaussian integers* in such a way that many of the familiar properties of the plain old integers are preserved, but it’s a little counterintuitive at first. The definition is that a+bi is even when a^2+b^2 is even (this is the norm of a+bi) and that a+bi is odd if it’s not even.
An answer from Mastodon that I shared here

So this got the old thinker ticking again. What if, I wondered, instead of 3x+1 or x/2, we used the complex numbers and went (3-i)x+1 and x/(2-0i) would that yield something interesting?

The Collatz Conjecture is that if you play a game where if a number is odd you times by three and add one and if even you divide by two that eventually you always get to one which loops to 4, 2, and back to 1. This is the only loop.

Test number 1 – powers of two

I asked Wolfram Alpha what 64/(2-0i) was. It is 32. Apply again and get 16. This seems to work all the way down.

Test number 2 – arbitrary odd numbers

I chose 7 – (3-i)7+1. The answer is 22-7i. That’s interesting.

Then I stopped and asked myself is 7 as a complex whatnot still odd? I asked what the complex conjugate of 7 is and, apparently, it is 7. So, I assume that’s the same as 7+0i but at this point, I clearly have no idea what I am talking about.

I’ve never let that stop me so let’s assume I am correct and have not utterly failed to understand some stuff.

7+0i is even if 7^2+0^2 is even. 49 is not even so, no 7 is not even on the complex doo-dah.

I’m not sure if this is good or bad but we have the Collatz step from 7 to 22 but with an extra -7i as baggage.

Test 3 – just run some numbers

I’m going to pick some smallish real integers and do this more complicated thing to them and see how long the real part stays correct for the simple version of Collatz.

Remember, I’m going (3-i)x+1 for complex odds and x/(2-0i) for evens.

7 -> 22-7i That’s odd for a complex number (the sum of the powers is 533)

22 should have gone to 11. Thus we have already deviated. Our new game leads us to 60-43i

And… I stopped.

First Conclusion

This game does not seem to play well over the complex plane. By “play well”, I mean do fun things.

Just out of idle curiosity, I asked what 22-7i over 2-0i was 11-3.5i. 11(3-i)+1 is 34-11i -> 17-5.5i…

Second conclusion

Well, I just got all excited over nothing. I truly hoped there was a nice pattern to find adding complex numbers to the Collatz thingy. Maybe there is but it might require writing some bad python to make a chart or something.

Ideas?

#CollatzConjecture #complexNumbers

Творческий коллектив Complex Numbers выпустил бету новой оперы 2084.

Опера состоит из 40 треков.

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