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Thursday, May. 9, 2024

3:30am 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 12 hours ago
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

about 17 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 2, 2024 at 9:48am

#1063315

Rats!

Despite the significance of the Great Groundhog today, we're going to talk about another rodent. The Platonic ideal of rodent, the Ruler of Rodentia:

In Defense of the Rat
They’re less of a pest than you think—actually, they have quite a few benefits.

Now, if someone had said that, say, mosquitos were "less of a pest than you think," I'd know they were bullshitting. But rats are cute, and don't we give cute critters the benefit of the doubt?

There was a time when we human beings used to put animals on trial for their alleged crimes against us.

Gosh, I wonder what would happen if they put us on trial for our alleged crimes against them?

The earliest of these prosecutions in the Western tradition of law appears to be a case against moles in the Valle d’Aosta, Italy, in 824 AD...

Another clear example of anti-rodent prejudice.

In the centuries between, a killer pig was dressed in human clothing and hanged in Falaise, France...

Okay, I can kind of see the pig wearing human clothing (just imagine Alex Jones), but how the hell do you hang a hog? They ain't got no neck.

...Marseille put dolphins on trial for crimes unknown...

That one's easy. The prince heir apparent of France was known as le dauphin. Someone mispronounced the definite article, and they thought they were trying les dauphins.

...and a rooster—in what must have been a case of mistaken identity—was burned at the stake in Basel, Switzerland, for the witchery of laying an egg while male.

Maybe he was just living his true life.

In 1522, “some rats of the diocese” of Autun, France, were charged with criminally eating and destroying barley crops. A skilled legal tactician, one Barthélemy de Chasseneuz, was assigned to defend the rats.

How come most of these are French?

Well. The article is fairly long, but I found it enlightening. Especially the part about how humans were a more proximate cause of The Plague than rats were: "In the case of the notorious plague in Europe, the event that forever marked rats as public enemy number one, the animals may be almost entirely innocent."

But there's also a long discussion about rats' intelligence and demonstrated capacity for empathy—not only with other rats, but with humans.

I'm not saying you should venture into the NYC subway tunnels and pick up a rat. There really are hazards with wild rats—just like there are with raccoons, and everyone thinks trash pandas are just the cutest things (mainly because they are). But I've known several rats in my life, albeit briefly (rodents don't tend to live very long lives), and, yeah... they're not all vermin.

Now, if I could only convince my cats to stop leaving them for me as gifts, that'd be great.

3 Like • Comment

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