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Tuesday, May. 7, 2024

5:15am 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

a day 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

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.

🌕 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

October 15, 2022 at 12:01am

#1039232

Reformation

Wrapping up October's "Journalistic Intentions"

[18+] with a blind quote.

"It is important to start socializing the idea of reforms now—sometimes they are upon us quicker than we think."

I have no idea what this is in reference to, and I don't want to look it up to do this entry. It's called a blind quote for a reason. I'm going to go ahead and assume it's referring to something in the US, though.

Consequently, no matter to what it refers, half the country stopped reading at "socializing" and immediately dismissed anything else. "Sounds like soshulizm to me."

I considered listing some issues that might need reform here, but there are so many things in that category in the US that it might be easier to list the things that are not in need of reform.

And if I had given myself more time, I might even be able to think of one. Thing is, when something is going right, we tend not to worry about it too much. This was the case with (yes, I'm going here) abortion laws, until suddenly it wasn't going right and it became something in need of reform.

The other problem with listing the things I think do need reform is that, inevitably, listing them creates the implication of some sort of order. Like, even if I say "in no particular order," whatever I list first will stick in a reader's mind as my top priority. If I say "police" first, you'll think that's at the top of my mind, for example. And now you probably already think it's police.

It is not.

And it's not like fixing one thing would make everything else fall into place. Well, with one possible exception: elections.

But that's still not the foremost problem on my mind.

Nor is education, nor space exploration, nor even the imminent threat of nuclear war. Not health care delivery (actual health care, now that I think of it, is one thing we do right—for those who can afford it). Not animal cruelty, not the environment, not climate change, not energy, not terrorism (domestic or otherwise), not gun violence. Even the problem of homelessness isn't the top issue for me; neither is inflation. Or the looming recession. Or living wages, or the existence of tipping, or lack of religious freedom. Racism (both systemic and personal), a general lack of affordable housing, Twitter, regressive drug laws (especially the continuing illegality of cannabis at the federal level), private prisons, infrastructure rot, drought, political corruption, and far more issues are certainly important, but again, I wouldn't put any of them at #1.

No, the biggest issue needing reform right now is the severe lack of beer in my refrigerator.

Fortunately, that one's easily solved, unlike these others, and I will do so later today.

What? With enough beer, I can pretend that these other problems don't exist.

Okay, now that I'm done, I'm going to Google the blind quote.

Huh. Supreme Court term limits and related reforms.

Just goes to show that, even when sober, I can't think of everything.

3 Like • Comment • View 2 comments

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