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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:

Kåre Enga in Montana

about 18 hours ago
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

about 22 hours ago
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

a day ago
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

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

August 8, 2021 at 12:04am

#1015284

Race to the Bottom

I'm not a person who seeks out instances of racism under every rug, but sometimes they smack you in the face.

4 Beloved Things ... That Have Surprisingly Bigoted Problems

Yes, it's another Cracked link. Such are the vagaries of the random number generator. That site's thing is countdown lists; one gets used to it.

4. Tattoos - People With Darker Skin Have To Deal With Shitty Artists

Everyone should have the right to make a terrible and permanent decision when they're newly 18 and deeply immersed in some fringe fandom or just after some really great sex. But for people whose skin tone resides in "can't find foundation at the drugstore" territory, it can be an annoyingly sensible process. If they just barrel into the tattoo shop, musculoskeletal guns blazing, it's entirely possible the artist on duty will explain to them that their options are severely limited, as colors lighter than their skin won't show up. Many refuse to work on them at all, including Ink Master season two winner Steve Tefft, who declared on camera, "I don't want the dark canvases. They take away half your skill set."

Or you could -- just spitballing here -- take the opportunity to improve your skill set. I don't have any tattoos for personal reasons (having none makes me unique), but an artist turning away people who want them because they can't be arsed to get creative with, you know, their artist job, just seems wrong.

3. Legalized Marijuana - Lots Of Green … For White Sellers

Entire articles could be (and have been) written on the intersection of racism and the prohibition of certain drugs, but now that weed is on the fast track to becoming the next booze (i.e., a perfectly legal pastime that just makes people really annoying), the shoe is on the other foot. And that foot is pretty well-heeled.

Most of the brewers I know are white, too. I'd be happy to see more diversity in either field, but you start to run into the usual racist problems: lack of general wealth, cops hassling darker-skinned people more (alluded to in the article) and so on. The lack of diversity in growers and brewers may be a symptom of this larger problem, not a stand-alone issue.

2. French Kissing - Was Just Regular Kissing Until American Prudes

Okay, so the French aren't exactly the most oppressed people in the West, but they're still the subject of scorn that honestly reflects a lot more on us than them. Take this whole "French kissing" thing. People have been licking each other in the mouth for thousands of years, but when European colonists showed up in North America, they weren't exactly sending their horniest. As a result, by the beginning of the 20th century, kissing with tongue had become so taboo that many people didn't even know it was a thing you could do.

Shh, don't tell them about "reverse cowboy."

American culture is, as you might tell by our dominant language, more derived from England than France, even though if it weren't for France we'd still be worshiping the Queen or whatever it is they do over there. And I don't know if this is true, but I heard that back in the early days of the Enlightenment, the French called syphilis the "English Pox," and the English called it the "French Pox." It sounds like something that should be true, anyway. We seem to have inherited the traditional English disdain for the French despite it being France that cozied up to us back when we were trying to stick it to the monarchy, after which they showed us what "sticking it to the monarchy" really meant.

1. Cryptocurrency - Another Reason It Sucks

When you picture a Bitcoin enthusiast, you're definitely thinking of a weirdly aggressive white guy, and there's a reason for that beyond their Elon Musk fan Twitters. Cryptocurrency has been dubbed "the currency of the alt-right" for reasons that no one understands but have something to do with it being decoupled from any government, and it's completely changed the economy of white supremacy, which is, ugh, yes, a thing.

I already hated Bitcoin and now I have even more reason to hate it.

Yes, two theater trips in one week. What can I say? I didn't have much to do yesterday, so I went to the drafthouse cinema.

One-Sentence Movie Review: Stillwater

This Matt Damon-led movie that you probably never heard of is surprisingly good -- what it lacks in plot advancement, it makes up for in acting, character development and scenery and I got through the slow parts by seeing if I could understand the spoken French without looking at the subtitles (it's set mostly in Marseille; the dialogue is mostly in English but I think the director wanted to demonstrate that the main character started out knowing maybe two words of French, so there are some French conversations and I understood about half of them).

Rating: 4/5

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