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Thursday, May. 9, 2024

12:22am EDT

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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:

Lazy Writer est 4/24/2008

about 9 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

about 14 hours ago
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

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

February 27, 2024 at 11:32am

#1064998

Olive It And More

To wrap up February's "Journalistic Intentions"

[18+]...

Olive

There's a grocery store on Broadway, on the Upper East Side (corner of 80th Street if you're ever in the area) called Zabar's.

I get the impression that it's moderately well-known across the land. Maybe it's been in a movie or show or two; I don't know. Maybe its vibe, which more modern and chain-affiliated places can't replicate with their corporate policies, focus on metrics, and eventual enshittification, is just something people respond better to.

Since I haven't been there in a while, I can't comment on their prices, but I remember them being about what you'd expect in Manhattan: slightly elevated, though not sky-high like in Hawai'i. But their location means they serve a moderately well-to-do clientele, which means offering some premium selections. The first time I went in there, I nearly dehydrated salivating over the seemingly endless, though really not because we're still talking about a Manhattan grocery store with limited space, selection of cheeses.

And then I saw the olive section and almost fainted from delight.

I like olives, you see. Not just black, green, and kalamata, but all olives.

Want to hear my most idiosyncratic quality? I don't think I've ever admitted to it in here before. Or anywhere online, really. I usually keep it to myself, because the one time I told someone in person, the look I got was so filled with horror and disgust, you'd think I made a habit of munching on baby sandwiches.

I get green olives on my pizza.

That's right. Pizza. New York slice, of course, with, at minimum, pepperoni and onions... and green olives.

I can't be alone in that, even if no one else will ever fess up. If I were, the local pizza shop wouldn't offer it as a topping, would they? And not just the local pizza shop, but the old one, the one that had been around since before I even got to town in 1983, the one that even more closely approximated NY pizza but sadly went out of business because of, well, you know—they offered green olives on their pies, too. Not just because of me, either; it was on the menu when I first visited each of them. Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives. But usually, they get it right, and they've never been out of stock (to be fair, the whole reason for green olives is preservation, so the little eyeballs might have been sitting around for years, for all I know).

Last time I went to pick up my extra cheese-pepperoni-onion-beef-jalapeno-green olive pizza at the place that managed to stay open, I recognized the owner as the one who provided the pie to me. "Ah, good! Green olives!" he enthused in his boisterous, Brooklyn-Italian accent. "You have wonderful taste!"

Finally, vindication.

1 Like • Comment

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