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Sunday, Mar. 9, 2025

9:39am 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:

Soldier_Mike

about 9 hours ago
In response to "Story Time"

Causation vs correlation. Reminds me of the phrases we've all seen here on site with respect to comma usage (e.g. Come down and eat, children! vs Come down and eat children!).

1 Like

tj wanderlust-words-in-motion

about 20 hours ago
In response to "Just Teaming"

What about "teamMe"!

When I hear "team player" I also hear the boss expecting everyone to give 110%, then going back to the office instead of pitching it.

2 Like

🌖 HuntersMoon

about 23 hours ago
In response to "Just Teaming"

3 Like

tj wanderlust-words-in-motion

a day ago
In response to "One Fine Thing"

Soldier_Mike

recently I asked on of my grandchildren if she new what an octothorpe was (she uses hashtag) and after a minute of deep thought replied, "A mythical creature."

1 Like

Soldier_Mike

a day ago
In response to "One Fine Thing"

Regarding your Exclaimer!, I never heard the term octothorpe before; it was, as you point out, either pound or number (sign) in my experience. As an aside, it's only visually similar to, not identical to and interchangeable with, the musical sharp sign. The octothorpe's left-to-right lines are horizontal, while the similar lines on the sharp sign are slightly angled from lower left to upper right (# vs ♯).

2 Like

tj wanderlust-words-in-motion

a day ago
In response to "Story Time"

It is amazing how you can give some people solid facts and they will doubt them, but make up a story filled with fallacies and they will believe it.

1 Like

Elisa, Stik of Clubs

a day ago
In response to "Story Time"

I might do my own commentary on this article, but for now, I will tackle one part.

The science of vaccinations and immunization schedules also seemed impenetrable. “I was very conflicted, and felt like: ‘I don’t know any of this stuff, I didn’t go to school for this,’” she says.

I struggle with this a lot. I really do. Part of me struggles because while science wasn't my strongest subject in school, I still did reasonably well in the various fields I did study. Biology happened to be my strong suit there, although I strangely managed to hold my own when I took intro to physics. That said, in my science education we didn't go over specific vaccination schedules or anything like that. However, between learning how vaccines worked and getting a halfway decent statistics education (a college semester and several introductory lessons in high school) I could draw the connection of vaccination schedules. So while people may think they didn't go to school for things like this...they might have without knowing it!

The other part of me wonders about the effectiveness of science communicators. This field admittedly is still pretty new (only gaining steam in the last decade). On the other hand, how effective are they in getting laypeople to truly pay attention? I feel like some of their work tends to kind of preach to the choir. I wonder if many of these communicators lean more on the science part rather than the communicating, and that's where things go awry.

4 Like

tj wanderlust-words-in-motion

Mar 6, 2025 at 1:59pm
In response to "Shhhhhhh"

I may have a slight allergy to delusional people; they give me a headache.

1 Like

Wordsmitty ✍️

Mar 6, 2025 at 12:40pm
In response to "Shhhhhhh"

I drove by that several decades back either coming or going to a vacation somewhere beyond. It's so strict that even birds couldn't tweet there. (someone had to say it)

2 Like

BIG BAD WOLF is Merry

Mar 6, 2025 at 9:29am
In response to "Shhhhhhh"

Always someone complaining about something, annoyingly.

1 Like

March 8, 2025 at 7:52am

#1085006

Just Teaming

First, an Exclaimer! ▼
EXCLAIMER
(explanation/disclaimer)

The theme for this round of Journalistic Intentions is "Banned Instagram hashtags! All of these will get posts shadow banned on Instagram." So there are a few things my readers should know:

#1- I do not have, have never had, will never have, an Instagram account.

#2- Consequently, I have no idea what a shadow ban is or what it entails, only that it has something to do with suppression of posts with the indicated tag.

#3- I do not acknowledge the pronunciation of the octothorpe (#) as "hashtag." That symbol is either "number" or "pound," and that's more than enough definitions for one character. Anytime I see the # with letters following, I pronounce it pound, which made #MeToo way more hilarious than it should have been.

However, I hold the belief that I can write about absolutely anything, regardless of prior knowledge. This contest round tests that conceit. All entries, including this one, were selected at random from the list of 16 prompts provided.

Journalistic Intentions (18+)
This is for the journal keeping types that come to PLAY! New round starts February 20!
#2213121 by Elisa, Stik of Clubs

#oralsurgeryteam

Whenever I hear or see the word "team," these days, I cringe. Partly, this is because of its association with sports, which I think need to be toned down some; there are other ways to practice competition and cooperation than ball-chasing. But mostly, it's because of the insistence that everyone be a "team player."

There is, of course, nothing wrong with being a team player. But too often, that's code for "give it everything you got so I can take credit and you get to keep your job."

It could be worse, of course; your boss could keep insisting that the workplace is a "family." That's even worse than a team, because at least with a team, you get to decide to go play for someone else or just walk away; options are far more restricted with family. And families can get pretty dysfunctional. Not mine, really, but in general.

I always wanted a mug or something with "I put the 'me' in 'team'" on it, but I never got one; I don't drink coffee anyway, and I eventually opted to just walk away.

But if you're going to insist on calling your workers a team, why not go all the way? Organize a football league. By football, I mean soccer; I'm afraid I'm being thoroughly internationalized. You can have the Oral Surgery Team facing off against the Grocery Workers Team, or the Emergency Room Team facing off against the Hardware Store Team.

I don't mean just sponsorships, either. When I tried playing baseball as a kid, I got assigned to the Hardware Store Team. We wore shirts with the giant logo of the local hardware store on the back. Which, as an aside, leads me to the other problem I have with sports, which is that they're often basically ads. Sometimes they're ads for a college or a city, but they're also ads for products. This is most obvious with car racing, which may not actually count as a sport because there's no ball involved, but does involve teams.

Anyway, yes, the players would be amateurs. That's the point. It's never enough to just have fun with your chosen hobby; you have to compete to see who's best, and the less-best get left in the dust. This was bad enough when competitions were local or regional, but now, with the internet, they're worldwide, and you're competing against 8 billion other people.

That makes it hard to really stand out, on a par with winning a lottery. But hey, sometimes you gotta take one for the team.

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