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Tuesday, Apr. 16, 2024

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

Elycia Lee ☮

about 2 hours ago
In response to "What's the Difference Between a Duck?"

So happy that there is an answer to that Alice in the Wonderland riddle.

Finally. Fascinating stuff. All of them. There is something rather philosophical about comedy. You are certainly right there.

Elisa the Bunny Stik

a day ago
In response to "That's Cole"

"I don't know what the latest fad food is, but I can almost guarantee that behind the fad is someone with money trying to make more of it."

I'd say there are multiple fad foods, including goji berries. That said, cauliflower became trendy in 2018 and has maintained some level of staying power. I still see cauliflower rice as an option in many places across the US.

4 Like

Elisa the Bunny Stik

Apr 13, 2024 at 6:10am
In response to "Mawwiage..."

"Or, at the very least, it's an emotional bond more than a business arrangement."

And for a substantial subset of parents, it's neither. They either just want kids to show off like trophies or dive headfirst into various forms of abuse.

3 Like

Aennaytte: Free & Wild in GoT

Apr 12, 2024 at 12:39pm
In response to "Coincidences"

Some words even cross species.

My golden cat calls me Mom frequently.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:58pm
In response to "A Cinderella Story"

Do you mean something like Carl having to work in the garage for his wicked step-dad while his brothers party? He was polishing an old hubcap that was magical and the next thing he meets a rich cougar at the club but has to leave by midnight when the spell wears off. As he exits he looses a boot. The cougar takes the boot with her and ends up having car problems the following day and stops at the garage where she notices Carl sweeping the floor with only one boot. She hands him the boot, it fits, and they are last seen sailing off on her yacht.

1 Like

tj ~ endeavors to persevere!

Apr 11, 2024 at 1:48pm
In response to "Things Go Better With Cahokia"

I bet they left because there wasn't anymore deer to barbecue.

2 Like

Robert Waltz

Apr 10, 2024 at 11:05am
In response to "Dark Side of the Moon"

⭐️Jellyfish⭐️

: Also known as a swag bag, but I usually prefer alliteration to rhyme (and also, since I pretend to be a writer, I like coming up with my own terms). No idea what you call them on that side of the pond. It's not technically "bling" because there wasn't any personal decoration, but it had things like certified sun-gazer glasses, a copy of their special eclipse bottle label art, a winery-logo corkscrew, and some delicious truffles (the chocolate kind, not the mushroom kind). Kind of like a Christmas stocking, but in April and for wine and astronomy nerds.

⭐️Jellyfish⭐️

Apr 10, 2024 at 8:18am
In response to "Dark Side of the Moon"

Wine, an Eclipse, and Pink Floyd Playing - Literally sounds like a Perfect Day!

And A Bling Bag! (Although not sure what this is, I am thinking a bag full of sparkly jewellery which it probably isn't)

1 Like

Kåre Enga in Udon Thani

Apr 10, 2024 at 1:34am
In response to "Dark Side of the Moon"

It's nice you took time out from you routine life and routine blogs. Mind you, routine has some appeal.

I saw the eclipse in 2017 in Montana. I'll probably not see another. Do I care? Well... if I happen to be near one... sure. I missed the lunar eclipse last year in Thailand and I wasn't happy... but I saw one in Venice (even saw Mars).

I agree that a sports venue has an ambience that one loses at an impersonal distance. I was in Allen Fieldhouse when Kansas won the national basketball championship in 2007. Not the same as being at the game, but close. 10,000 fans created some ambience. And the town afterwards? Incredible!

Video is visual/audio at best. But what is the smell, the touch of a breeze, a hot dog or the taste of wine on the lips? Also... one only sees/hears what others see/hear. I want to have my own experience.

Songkran is soon, in three days. I dread it in some ways, but it may be a break from the ennui of hot at night and worse by day.

1 Like

Kåre Enga in Udon Thani

Apr 10, 2024 at 1:20am
In response to "Louisville Sluggard"

I'm very light sensitive...

I don't see much under $100/night and very little over 8.0 that I can afford. Most of the nice places are around $200/night ... or ... what I pay for one month's rent here in Udon Thani.

Why don't I travel the US? 1. Don't have a car. 2. Can't afford it.

1 Like

October 30, 2019 at 12:05am

#968631

The King's English

Well, I've signed up for "30-Day Blogging Challenge ON HIATUS"

[13+] again, for November, since I'm not doing NaNo this year. Once again, I figure if I'm going to try to write something in here every day, might as well mix it up with some prompts I wouldn't consider on my own.

Meanwhile, I still have a ton of blog fodder to get through. Here's today's:

https://cheezburger.com/9184517/the-english-language-being-infuriatingly-confusi...

The English Language Being Infuriatingly Confusing (39 Images)

By "images" it means "screenshots of tweets." I despise Twitter with the fiery passion of 10,000 suns, but sites like this (as clickbaity as it is) can sometimes present the best of the worst.

Since they're screenshots, copy/paste isn't an option, so I'll just pick a few amusing ones to highlight.

#8 It blows my mind that english has no plural for "you."

Ah, but it does, at least here in the South. "Y'all" is a perfectly good second person plural. It sounds more polite than "youse guys" (NY/NJ) or "yinz" (specific to the Pittsburgh area).

Incidentally, it's always "y'all" and never (as I've seen it) "Ya'll." An apostrophe stands in for missing letters, and the missing letters in this case go between the y and the a, not the a and the l.

And yet, even if you avoid regional dialect and think only of Standard English, the plural "you" still makes more sense than the French "vous," which can be either a second person plural, or a formal second person singular. How do you know when you can drop the formal "vous" and use the familiar "tu?" I guess I'll have to spend some time in France to figure this out. Awww.

#9 Defenestration

Still one of my favorite words.

#11 Why does my nose run but my feet smell?

You might wanna see a doctor. Or three.

#22 I before E except when you run a feisty heist on a weird foreign neighbour.

Yeah, okay, that one's an example of why English is frickin' weird.

#26 The fact that Kansas and Arkansas are pronounced differently bothers me way more than it should.

This might have been my introduction to the fuckeduppedness of the English language. To this day, I pronounce Arkansas "ar-Kansas" just to be funny. I also pronounce Missouri "misery" because it's Missouri.

#33 Why is a "w" called a "double-U" when it is clearly a "double-V"?

Not in cursive. Also, because in Latin, from which we derive our alphabet, V is U. Confused yet?

Anyway, those are just the short ones. The longer ones are worth reading, too. I'm now even more convinced that English has been dominating the world stage not because of British colonialism or because it's versatile, but because once you learn English you feel a sense of pride unmatched by learning any other language (except, perhaps, Mandarin, though I wouldn't know). Once you've learned to navigate its dark corners, there's no going back.

3 Like • Comment

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