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Monday, May. 6, 2024

12:04am 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 15 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 21, 2023 at 9:03am

#1049920

Revisited: "Naturally"

Spinning the dials on the ol' time machine, today we land on "Naturally"

, from just over two years ago.

The entry was a 30DBC response, and the prompt was: Write about your favorite outdoor activities to do in the summer. Are there any activities you haven’t done that you want to try?

I have a distinct memory of shuddering when I first saw that prompt. I have a bio somewhere—not on a dating site, because I don't do dating sites—that describes me as a "dedicated indoorsman."

So, I opted for humor; specifically, hyperbole:

Well, my only favorite outdoor activity in the summer is: rushing from an air-conditioned car into an air-conditioned bar; if the accursed daystar is burning, add "while shading myself as much as possible."

And that's not entirely true. I rarely drive to bars, on the theory that I might have to leave my car there to Uber home, thus necessitating another trip, the next morning, while hung over. So the "car" in question is a rideshare.

I'm just as likely to walk to the bar. This is true no matter the outdoor temperature. That doesn't mean I'm enjoying the outdoors; it just means I'm a cheapskate.

Still, given a choice between being too hot and too cold, I will pick too hot every damn time, so if I'm going to do anything outside, it'll be in the summer. Of course, one is never given such a choice; either it's winter and too cold, summer and too hot, or a week or so in between when it's actually pleasant to be outside for five minutes when it's not raining.

This is only a slight exaggeration. We usually get more than a week of mid-range temperatures. Sometimes as many as two!

But this does give me the opportunity to talk about a phrase that triggers my grumpiness, to a possibly irrational degree: when someone says something like "I'd rather it be cold because I can always put on more clothes, but there's only so many I can take off."

It's not that those people are different from me. As with being a morning or night person, people prefer different things and it's hard to change that, even if I wanted to, which I don't. If this weren't the case, we wouldn't have people living in Alaska or, conversely, Arizona. So, okay, you prefer the cold; that's good to know. We can be friends, but we'll never take a Caribbean cruise together.

I think it's partly the implied naughtiness: tee hee, now you're picturing me naked. Thanks, I'm already doing that (if you're female) or repulsed by the idea (otherwise).

Worse, though, is that it's dead wrong.

Ever seen people adapted to extreme heat? I don't mean the scantily-clad jungle-dwellers of various tropical societies; they've usually got some shade to cool off in. I mean, like, the desert-dwellers, the real-life inspiration for the Tusken raiders of Star Wars fame. Do they run around mostly naked? No, they're completely covered in loose-fitting clothing. This serves as portable shade and takes advantage of the slightest breeze to provide evaporative air conditioning.

And for me, when it's cold, it doesn't matter how many layers of clothing I wear; I'm going to freeze anyway. Once my hands or feet are cold, that's it. I'm done. If I wear enough clothing to delay this freeze, I'm uncomfortable and can barely move.

So I prefer to do as nature intended, stay indoors and run my A/C in the summer and heating in the winter. Yeah, compared to the vast bulk of humanity, both now and in the past, I'm living in privileged luxury. So? Might as well take advantage of it.

No, I'm of the firm opinion that we evolved to build shelters for a reason, and that reason is that so we could use them. Don't get me wrong; I love nature. I'm a big fan of watching webcams of natural areas.

And that's an excuse to re-link the webcam I talked about in that entry, since we're coming up on the summer solstice once again: The Brooks Falls Brown Bears

from Alaska.

2 Like • Comment • View 1 comment

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