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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 4, 2024 at 10:43am

#1076238

Isn't It Draconic?

"Blog Week Birthday Bastion 2024"

[13+] by WakeUpAndLive~"HoHoHo"

Prompt 4. Sept 4.

Photo prompts. (Choose 1,2,3 or 4 and write fiction or non-fiction)

PhotoPrompt 3

Photo Prompt 3

I'm only posting the prompt pic I picked. One of the others was a blue rubber duck, and I almost picked that one, but dismissed it as "too cute."

Ducks and dragons are related, though.

A drake is a male duck. A drake is also, depending on the source, a particular subtype of dragon, or a synonym for dragon. The latter has a different etymology, one which is more apparent when you consider the adjective form, "draconic."

That should not be confused with "draconian," which is used to describe oppressive policies. Nor should it be confused with the explorer Sir Francis Drake, or his namesake Frank Drake, originator of the Drake Equation, which has nothing to do with dragons. Unless aliens are dragons. Which isn't technically impossible.

Another synonym for dragon is worm, or wyrm, which also confused me as a kid. English is weird.

Dragons are, unlike ducks, creatures of fantasy. Unless you count Komodo dragons, though I say that's cheating. But I have this hypothesis that dragons were dinosaurs.

Why were dragons part of the folklore of several geographically separate cultures? I think it's because of dinosaur bones. Some ancient t-rex or brontosaurus skeleton or whatever got exposed via erosion. Early humans, clever and creative but without our understanding of geological time, might have seen these enormous bones poking out of some sedimentary rock, and pictured what sort of creature might have made them. Clearly, it was a giant, flying, fire-breathing, gold-hoarding monster, because what else could it be?

But also, ducks are dinosaurs.

All birds are. Lots of dinosaur lineages indeed went extinct, but at least one survived into modern times and their genetically-plastic descendants exploded into the vast diversity of avian species we encounter today. Those eggs you had for breakfast? Dinosaur eggs. That KFC bucket you reluctantly bought over the Labor Day weekend? Kentucky-fried dinosaur parts.

Don't feel bad about eating chicken. Their ancestors probably munched on ours. Colonel Sanders was just doling out payback.

So, if you're wondering what a dragon would taste like... well, it would probably taste like chicken.

Or duck.

Unlike our modern birds, though, dragon meat might even come pre-cooked. All that fire breath had to do something to their insides, right?

Let's do this again. We get to give out a free Merit Badge every day this week. Want one? Anyone who comments here before 11:30 pm WDC time today could get today's. (I'll need that extra half-hour to pick a winner and send the badge before midnight.)

To clarify:

When I say "comment," I mean comment. Not review. Though reviews are always welcome.

I also mean "here," not on the newsfeed post.

MB recipient will be chosen at random.

Maximum of one MB per commenter for the week.

If I don't get comments, I'll pick a previous commenter, and maybe not at random.

The MB will be the one I commissioned two years ago, "Complexity," which is a publicly available MB.

I appreciate all comments; this is just a little incentive.

5 Like • Comment • View 7 comments

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