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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

May 17, 2024 at 6:57pm
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

November 15, 2020 at 12:01am

#998384

Good Enough

Well, this is a trick question.

PROMPT November 15th

What does “a good life” mean to you?

The reason it's a trick question is that "good" has too many definitions.

It can indicate a desirable state: good news, good quality, a good road, etc.

It can demonstrate a subjective opinion: a good movie or book, good food, whatever.

It's a moral judgement: she's a good person, he does good deeds.

It describes an emotional or physical state: she feels good, he looks good, a good time.

It indicates skill: he's good at writing, she's a good painter.

It's a simple compliment: You're a good kitty. (I say this a lot even when it's not strictly true.)

And there's probably more, including the (mis)use of it as an adverb, substituting for "well," as in "You cook really good."

French is no help in this regard, by the way. You can translate "good" into several different words, and I'm rarely sure when to use, say, "bon" and when to use "bel." I may never figure it out, but someone's got to annoy the French and it might as well be me.

So asking me what "a good life" means depends entirely on context. Are we speaking ethically or materially? Is it a matter of something that happens to you or something that you have to work for?

Change the article in the phrase and you also change the connotation: "a good life" can mean something different from "the good life." Une bonne vie, la belle vie.

Fortunately, as a writer, such ambiguity is a benefit, although I haven't delved into it until right now so my thoughts aren't fully formed. But if I were to plan out a story entitled "A Good Life," I might contrast the life of someone dedicating their actions to helping others, and someone living a life of leisure and luxury (which, contrary to popular belief, does not preclude also helping others). In other words, one living to do things for others, and the other living for the pleasure of it. I'd want to show, in such a story, that both individuals are pursuing their own idea of pleasure, though Other People are going to hold the first person in higher regard than the second... which is, of course, selfish on the part of Other People because they're the ones benefiting from it.

Put another way, Person A pursues charity and derives pleasure from helping others, while Person B pursues comfort and derives pleasure from leisure. (You, uh, should read that last phrase in a British accent for best effect.) We say that Person B is selfish, but the only real difference between them is the actions they do to satisfy themselves -- and how those actions are perceived by others.

Honestly, I'd choose a mix of both -- like I said, they are not mutually exclusive, though in our binary-loving society people tend to think in extremes and exclude the middle. I've noted before the false dichotomy in the sentence: "It is better to be poor and happy than rich and unhappy." ("Better," you'll note, is the comparative form of "good.") It is a false dichotomy because a) it's possible to be poor and unhappy; b) it's possible to be rich and happy and c) from the original choices, I'd personally rather be rich and unhappy.

But, if I were forced to pick from one or the other, I'd choose "a good life" as in a life of comfort, luxury, travel, gourmet food, expensive scotch, delicious beer, and all the finer things. That's good enough for me. Those who don't see that this also helps other people along the way might benefit from a good course in economics.

9 Like • Comment • View 8 comments

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