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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 13 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 18 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 18 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

a day ago
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

September 22, 2024 at 2:16am

#1077115

Landmarks

I don't use fitness apps, so I have no idea how many steps I took yesterday, or how many kilometers they added up to. But both numbers were very, very high.

While I was still exhausted from the trip, my contact here texted me around lunchtime. We'd never met. A mutual friend introduced us. It's probably only the mutual friend that kept us from going "what if the other's a psycho killer?"

Anyway, she's like "I'll be at [landmark] and we can meet at 1 o'clock." (She's American, incidentally, so we're texting in English.) At that point, it was 12:10. I checked Maps. Walking to [landmark] would take 45 minutes. I can just make it...

...except that I'd be walking through one of the most historic and architecturally interesting parts of Paris, and there is no way I would be able to resist stopping and gawking at something. Especially when the destination was on the other side of the Seine, and what foreign tourist can NOT stop and look at the river while crossing it? Maybe someone with more self-control than I have, but certainly not me.

So we met here at the hotel and started walking. I won't bother you with all the world-famous shit I saw yesterday, but there was a lot of it and it's world-famous and it's still thrilling to see that shit in person. Just one example: my hotel is a couple of blocks from the Louvre. Well, a couple of blocks from one corner of it, maybe a kilometer from the opposite corner. It's that big. Even without going in, the building itself is a work of art. And we didn't go in anywhere; it was Saturday and the tourism was in full force, creating chaotic crowds.

Hours later, we parted, and I made my utterly exhausted way back to the hotel. Along the way, though, I paused to snap a picture of perhaps the most culturally significant of all of Paris' landmarks, located on Rue de Rivoli.

Because, though I may have gotten some of the details wrong, it was here where, sometime around 1990, famed American visitor Vincent Barbarino discovered that, in France, a Quarter Pounder with Cheese is not, in fact, called a Quarter Pounder with Cheese, but a Royale with Cheese. Because of the metric system. These events were related in the documentary, "Pulp Fiction," which depicted quite the embarrassing and tragic ending for Vincent, but at least he got to spend time in fine Parisian restaurants.

6 Like • Comment • View 2 comments

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