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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

tj-Merry Mischief Maker

about 17 hours ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

July 25, 2024 at 12:13pm

#1074374

Let Me Give You a Hand

Wrapping up this round of "Journalistic Intentions"

[18+] with the final randomly-selected prompt:

Antwerp

And seriously, I used a random number generator. It's pure chance that it landed on a city in Belgium at a time when I'm planning a trip to France and Belgium.

And I'd love to visit, really, I would. The city hosts the Bollekesfeest every year, which features local beer; if you need to know anything about me at all, it's that Belgian beer is my Kryptonite. Sadly, the event takes place in August, and the timing doesn't work out for me. And it's home to the Antwerpse Brouw Compagnie, which I've heard brews a beer called Seef or Seefbier whose origin dates back to the 16th century. For context, that was before European colonization of the Americas. Hopefully the beer itself isn't that old, but damn, it sounds like something I need to try. (Their more modern brews look awesome, too.)

The problem is I don't have unlimited time. Tant de bières, si peu de temps. Yes, that's French, though Antwerp is in the Dutch-speaking part of the country. Hell, it's practically Nederland, another country I'd love to visit. My primary interest in Belgium this trip is their famous abbey breweries. Monk beer. So, Brussels and maybe Bruges. I think. Yes, I'm aware that Brussels and Antwerp are quite close together, maybe 40km; I'm perfectly capable of reading a map. There's still not enough time to do everything.

Besides, I gotta save some cool stuff for the next trip.

And no, I still haven't picked up much of the language. I tried. It's harder than French, because it's simultaneously very similar to English and very, very different. All of the Dutch-speaking people I know have perfect English, and it's embarrassing that I can't seem to return the courtesy. Well, maybe not "perfect" English (because such a thing does not exist), but still better than that of most Americans.

As you know if you've been following along, one of my other interests is etymology, and the origin of the name "Antwerp" is debatable. But, like Rome, in addition to the actual etymology, it has a mythological etymology, and it's glorious.

I'll just let Eupedia

relate it:

The legend says that the name 'Antwerp' comes from the Dutch "hand werpen" meaning "hand thrown".

The story has it that a mean and nasty giant controlled the river traffic, demanding exorbitant tolls. Those who refused to pay had one of their hand cut off.

But one day, a young and brave Roman soldier named Silvius Brabo managed to kill the giant. He cut the giant's hand and threw it in the Scheldt River, giving the city its name.

I need details, dammit. How did Silvius Brabo defeat the giant? More importantly, how did he keep the giant from landing on him when he killed it? I did find that the giant's name was Antigoon, which somehow doesn't mean "he who fights against goons." And is this the first example of classic rent-seeking

behavior and its inevitable consequences?

Sadly, the likely actual origin of the name is far less interesting: "The name comes more probably from the word ‘aanwerp’ (alluvial mound’), which describes the first settlement's geographical feature." (Same Eupedia source as above.) Yeah, apparently "werp" served double duty, much as its English descendant "warp" does. Though one could make the argument that the alluvial soil was "thrown" there by the river, I suppose.

And now I want to visit Antwerp more than ever. Dammit. I don't have infinite funds, either. Maybe I can start charging tolls.

5 Like • Comment

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