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Sunday, May. 5, 2024

5:21pm 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:

🌕 HuntersMoon

about 9 hours ago
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

about 24 hours ago
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.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

April 4, 2021 at 12:01am

#1007712

Past Intense

It always bugged me when people would romanticize the past. I mean, okay, technically, there was a period called the "romantic" period, and look, let's face it, "romantic" has WAY too many definitions, mostly incompatible with each other.

What I mean is the people who look at the past all starry-eyed and breathless and go, "I wanna live THEN." And look, I've had friends in the SCA, I read and write fantasy, and I play fantasy role-playing games. Know what all of those things have in common? "Fantasy." I can still take advantage of modern sanitation, electricity, and medical facilities.

Leave it to Cracked to make a numbered list of exactly why the past completely sucked syphilitic ass.

55 Facts That Show The Past Was Absolutely Gross

Aren't you happy to live in the modern, hygienic world that exists today? A world where you can easily wash your hands anytime you like, and must disinfect yourself with sanitizer every time you enter a building, and wear a mask to limit germ transmission, and submit to continual temperature checks in order to walk around publicly ... uh, all right, some of this might feel a tad excessive. But wow, is it infinitely better than the alternative you'd have to deal with if you lived centuries ago.

Okay, so maybe the present isn't exactly what you'd call "perfect."

I won't be copying all 55 of these. Of course. Go check out the link to find examples even more egregious than the ones I'm highlighting here. Especially the first one, which I'm going to skip right over.

2. Cat Piano

Johann Christian Reil arranged cats so hammers hit their tails, and they would cry out. Somehow, this was supposed to jump-start patients back into sanity.

I don't believe in an afterlife. But if I'm wrong, I want it to be run by cats, with this guy hit eternally by hammers. On his "tail."

11. Splinter Butt

Before we settled on toilet paper (or the convenient anal hose), people as recently as the 1930s were wiping themselves with rough stuff that gave them splinters.

About a year ago, this was looking like it was going to make a resurgence.

17. Fire Toilets

Roman toilets would occasionally erupt in open flames.

Huh. I didn't know they had Chipotle back then.

21. Castration Cults

Rome had a cult based on the Greek goddess Cybele, and adherents modeled them after her consort, a eunuch.

Yeah, that's a truckload of nope right there.

30. Gong-Farming

Someone had to clean out medieval cesspits. That job fell to the gong farmer, who would have to jump into the pit to shovel the stuff into a bucket.

And I thought my job, which sometimes involved investigating sanitary sewer pipes, could suck.

33. Werewolf Trials

Along with the very reasonable fear of witches, Europe in the 15th and 16th centuries suspected people might be werewolves. Thousands were executed for this offense. Circumstantial evidence included proximity to tomatoes.

Hey, I was just trying to enjoy my Big Mac in peace.

42. The Big Stink

In 1858, the Thames got clogged with sewage, a heatwave set in, and the smell was so bad, Parliament had to relocate to a rural area upstream.

Odd how one never sees that year on Doctor Who.

Now, I'll admit that there are some things from the past that we might do well do emulate. After re-reading that list, however, I'm hard-pressed to think of a single one. So as much as this past year has been no fun for just about everyone, at least we're not taking shits in exploding Roman latrines and wiping our char-broiled butts with splintery wood.

Yet.

1 Like • Comment • View 4 comments

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