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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:

Aiva Raine

a day ago
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

June 9, 2023 at 7:44am

#1050848

Plie

Another one for this month's "Journalistic Intentions"

[18+]...

Plie

I don't know everything.

This certainly comes as a shock to some of you, but it's true.

Usually, when there's a term I've never heard before (like plie) I take advantage of living in a pre-apocalyptic technological society and Google it.

But sometimes it's more fun not to.

The only clue I have is that the word is in the "dance" section of the JI prompt list. This may also come as a shock, given my name, but I know almost nothing about dance. It exists, and some people (who are not me) take great pleasure in performing or observing it.

My ex was (maybe still is; I don't know) a belly dancer, so I'm not completely ignorant of the art form. I know that they have names, usually derived from non-English words, for certain moves. I don't remember any of them, though.

I do have some small knowledge of French, which lends names to some aspects of dance (ballet, e.g.) but I don't recognize "plie" from my limited Francophone vocabulary.

So, to me, even though my eyesight is pretty good again a year and a half after cataract surgery, it just looks like someone misspelled "pile." Hell, my browser's spellcheck doesn't even recognize the word. It suggests, in this order: Pile, pie, lie, plies, and plied.

The latter two are pretty obviously present and past tense, respectively, of the word "ply," which has several meanings.

For one, as a noun, it refers to laminated or layered material. Like plywood. Or 2-ply toilet paper. Neither of which is directly related to dance, unless you're doing it on a plywood stage and/or acting like a mummy. Which is something different from a mummer, who can be, in fact, a dancer. I suppose you can get "plies" and "plied" from it, but that would be an odd construction in English.

As a verb, one can ply a a trade or profession, or ply someone with questions to try to pry information out of them. There are some less common usages, but they're all shortened from "apply."

One other option that doesn't come up in spellcheck suggestions is "plier," which can mean one who plies (as in the above verb) or the never-used singular version of "pliers," a grabbing tool that has two parts, so that when I was a kid, I imagined that "plier" was one branch of a broken pair of pliers (see also "scissors").

English is weird.

Despite its use as a prying tool (maybe it should have been called "priers" instead, resemblance to "priors" be damned because there's plenty of those homophones around), the noun form of "ply" comes from the French "plier" (which I'm guessing is pronounced plee-ay), which means something like to fold.

And with that, I think I'm close to the meaning of "plie": something to do with folding oneself. Let's check our work:

plié: a movement in which a dancer bends the knees and straightens them again, usually with the feet turned out and heels firmly on the ground.

Okay, I was thinking bending at the waist, but fine. Now I know. It's not like I haven't seen ballet before (I just don't know the words), and that seems to be a pretty common move. Doesn't look a lot like folding, though. "Bent" (past tense of "bend") is probably a better translation.

Now, see, I could have gotten there more quickly if the accent aigu (é) had been, in the first place... applied.

4 Like • Comment • View 1 comment

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