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Monday, May. 6, 2024

4:46am 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 20 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

a day 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

May 18, 2023 at 6:11pm

#1049803

Legally Binding

While one should never get their legal advice from an online comedy site, you might like this Cracked article about laws.

5 Uniquely American Laws That Other Countries Don’t Seem To Need

Yeah, I don't know if these are unique. And it's not like other countries don't have stupid laws, too. Hell, some of them still punish you for blasphemy.

The United States is a pretty weird country.

Which one isn't? Oh, yeah, Canada. Never mind.

Even though what’s supposed to be the famous, usually screamed tenet of America is freedom, the actual freedoms we do and don’t have are cherry-picked and puzzling.

Yeah, right. "Freedom."

So it’s unsurprising that there’s a whole lot of regulations and laws in the U.S. that haven’t fallen far from the apple tree — at best confusing, at worst fully oxymoronic.

Or just moronic.

Here are five American laws that are likely, in the eyes of other modern governments, incredibly dumb.

I always liked those lists of weird laws still on the books, like needing a license to wear penny loafers, or whatever.

These aren't those, though.

5. Female Lawmakers’ Backwards Dress Codes

Another point on the high school side of the scale is the fact that, despite being our chief legislative body, Congress still enforces a fucking dress code. And like most dress codes, it’s a whole lot more draconian when it comes to the female members.

That's idiotic, sure, but then there are still countries where "female lawmaker" is semantically and legally impossible.

Sure, Britain isn’t much looser, but they also think “fanny” is a cuss, so is that such a win?

That's what I've been saying.

4. Kinder Surprise Eggs Banned

Another common feel in American law is the conflict between a country that’s supposed to be advocating for freedom above all, while seemingly convinced that every American has the death drive of a baby lustily staring at the forbidden liquids beneath the sink. One place this pops out is in the absence of the Kinder Surprise Egg in American stores.

Meanwhile, far more hazardous products remain legal. You know what I mean.

3. Weird Real Egg Laws

Right, because no one else has weird laws about food.

2. Pharmaceutical Advertising

Everywhere else foolishly believes that if you need medication, your doctor probably isn’t relying on you to provide suggestions. It doesn’t help that the advertising is just as predatory as usual, mostly suggesting that if you don’t fix your allergies, your child will spit on you and leave you to cry in a musty robe while they go to the park to play with their other parent, who they now like more.

I despise almost all advertising, and it is kinda strange to push prescription medicine on the TV, but there are worse things to advertise. Homeopathy, e.g.

1. Sex With A Porcupine

And I'm done with the internet for today.

6 Like • Comment • View 2 comments

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