Complex Numbers (Book)

Blog Calendar

◄ October ► 2022
S	M	T	W	T	F	S
						1
2	3	4	5	6	7	8
9	10	11	12	13	14	15
16	17	18	19	20	21	22
23	24	25	26	27	28	29
30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 29, 2022 at 12:01am

#1039887

A Positive Thing

"Hey, Waltz, you should do another article on something that's positive."

Here you go. You should get a charge out of this:

Inside the Proton, the ‘Most Complicated Thing You Could Possibly Imagine’
The positively charged particle at the heart of the atom is an object of unspeakable complexity, one that changes its appearance depending on how it is probed. We’ve attempted to connect the proton’s many faces to form the most complete picture yet.

I don't know; the most complicated thing I can imagine is a romantic relationship. A proton ain't got nothin' on that.

More than a century after Ernest Rutherford discovered the positively charged particle at the heart of every atom, physicists are still struggling to fully understand the proton.

Maybe their attitude is too negative?

High school physics teachers describe them as featureless balls with one unit each of positive electric charge — the perfect foils for the negatively charged electrons that buzz around them.

You know, I kind of understand why the protons in a nucleus, all positively charged, don't fly away from each other: it's because on small scales there's another force stronger than electromagnetism that binds them together. What I never did get is why, since positive and negative charges attract, the electrons stay in a probability cloud around the atomic nuclei instead of just slamming into the protons.

It's not really analogous to planets orbiting the sun, though that's the model they teach you in elementary school. The reason is some really damn complicated quantum shit that I don't understand. Apparently it takes a hell of a lot of energy to get them to actually collide (this is alluded to later in the article).

Getting back to the subject, though:

College students learn that the ball is actually a bundle of three elementary particles called quarks.

Which I really don't understand. But it's still fun to say.

But decades of research have revealed a deeper truth, one that’s too bizarre to fully capture with words or images.

Because of course.

As the pursuit continues, the proton’s secrets keep tumbling out. Most recently, a monumental data analysis published in August found that the proton contains traces of particles called charm quarks that are heavier than the proton itself.

And that, dear readers, is deeply, deeply weird. I mean, quantum anything is pretty weird, but that goes way beyond weird. There's not even a word for how profoundly, utterly, mind-blowingly strange that really is.

Proof that the proton contains multitudes came from the Stanford Linear Accelerator Center (SLAC) in 1967. In earlier experiments, researchers had pelted it with electrons and watched them ricochet off like billiard balls. But SLAC could hurl electrons more forcefully, and researchers saw that they bounced back differently. The electrons were hitting the proton hard enough to shatter it — a process called deep inelastic scattering — and were rebounding from point-like shards of the proton called quarks. “That was the first evidence that quarks actually exist,” said Xiaochao Zheng, a physicist at the University of Virginia.

Always nice to hear from my university. (Except of course when they beg me for money.)

Incidentally, you might want to go to the link to look at the helpful pictures.

But the quark model is an oversimplification that has serious shortcomings.

Because of course.

The rest of the article describes the experiments and what they're finding, and I certainly think it's fascinating in addition to being really quite incredibly weird. I won't transcribe more, because it's Friday night and I have other things to do. But it's absolutely worth a look, even if you don't fully understand it.

I sure as hell didn't.

Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.