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Thursday, Mar. 6, 2025

2:10pm EST

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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:

tj wanderlust-words-in-motion

11 minutes ago
In response to "Shhhhhhh"

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

1 Like

Wordsmitty ✍️

about an hour ago
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

about 5 hours ago
In response to "Shhhhhhh"

Always someone complaining about something, annoyingly.

1 Like

tj wanderlust-words-in-motion

about 20 hours ago
In response to "Now, That's Using Your Noodle"

I wish my ex-mother-in-law could have read this, her idea of perfect pasta was when it went fully limp and flat! Of course, even if this was presented to her, it wouldn't help, another of her cherished traits was you couldn't tell her anything.

1 Like

Annette

a day ago
In response to "Now, That's Using Your Noodle"

My French grandmother had zero advanced degrees in anything, but every single meal she has cooked in her life would put these scientists as well as every single Michelin starred chef back into his little corner.

I bet that there were and still are billions of women making daily delicious dishes without needing a PhD.

These men made it their profession to play with food, only to come to the conclusion that they need to shut up and give compliments to the real chefs of the world.

I know there is the occasional woman who doesn't care for cooking. But they also don't go around meddling with others' cooking skills.

2 Like

Adhere - Definitely Writing

a day ago
In response to "Now, That's Using Your Noodle"

Your research trip sounds important - if you get funding I'd volunteer to come along as a research assistant - I think we should definitely look at the 'perfect' wines to accompany pasta dishes - which would take simply ages to determine.

3 Like

tj wanderlust-words-in-motion

a day ago
In response to "Stress Marks"

I agree, there are many ways to indicate stress in writing; there's no reason to get stressed over it. Just stay constant or you may stress out your readers!

BIG BAD WOLF is Merry

Mar 4, 2025 at 10:51am
In response to "Stress Marks"

There's always something that one can do.

tj wanderlust-words-in-motion

Mar 3, 2025 at 4:36pm
In response to "Life As We Don't Know It"

There's probably a sign at the edge of the Milky-Way that reads, "Caution, enter at your own risk!"

1 Like

Annette

Mar 2, 2025 at 2:18pm
In response to "Revisited: "Real Men of Genius""

My second son was born at almost the exact same time as one of my uncles died. When second son was a baby, we looked out for signs whether there was some reincarnation going on.

If there was, then he is a great example of nurture versus nature. Where my uncle was creative, sensitive, and mentally destroyed by the time he was a teen, my son's creative side is thriving, he has turned his sensitive nature into a passion for anthropology, and he knows he is loved unconditionally.

Maybe reincarnation is simply one generation deciding to put a stopper on past generations' bad habits.

1 Like

March 6, 2025 at 8:21am

#1084882

Shhhhhhh

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

#stop5g

There is a town in West Virginia, not too far from where I live across the state line, called Green Bank. Green Bank was apparently named after the green bank of a nearby river; as with many such names, I think you'd be unsuccessful in finding any such greenery. Kind of like how a subdivision is defined as a place where they cut down all the trees and name the streets after them.

The reason Green Bank is known outside of an obscure county in an economically depressed area is because of the Green Bank Telescope, a large radio telescope used for astronomical observations and probably sneaky spy stuff too.

Thing is, radio astronomy is notoriously subject to interference from Earthbound electromagnetic radiation. I say "electromagnetic radiation," because that's what it technically is, but it unfortunately contains the word "radiation," which is ooga-booga scary. The light that we see is technically radiation, and it's mostly harmless—we don't put on sunscreen to shield ourselves from visible light, but from invisible ultraviolet. So, yes, some portions of the EM spectrum are harmful. Some are not. Has to do with wavelength and energy.

So Green Bank, WV is part of the National Radio Quiet Zone,

a fairly large area with restrictions on what EM devices are allowed to operate. The NRQZ is fairly large; its edge is, in fact, within easy walking distance of my house in Charlottesville. The closer one gets to Green Bank, the more restrictions; in the town itself, you're not allowed to use microwave ovens, Wi-Fi, or cell phones.

For some people, I know, that sounds like Paradise Itself. Reportedly, some people have moved to the town solely because of their delusional belief that they're allergic to EM waves.

For me, that would be the Third Circle of Hell. Yes, only the third; I can think of worse places to live than West Virginia. I know I shouldn't say that as a lifelong Virginian, but yes, objectively, there are worse places. Cleveland, e.g.

But, despite the relatively minuscule number of crazies flocking to GB to escape the evil waves, there are a whole lot more people who bought into the lie that 5g cellular networks are dangerous. And those people are everywhere. If you don't have good mobile service in your area of the US, and it's not part of the NRQZ, you can blame them. And you can also blame the people who want good cell coverage, but refuse to allow towers in line of sight because they're "ugly."

Sometimes, the NIMBYs get compromised with cell phone towers that are camouflaged to look like very tall trees. You see them sometimes from interstates: rising mightily over the surrounding forest, a few desultory green branches stuck into the tower's structure. They don't fool anyone. They're like incompetent snipers in ghillie suits.

Every time I see one, whether I'm driving alone or with someone else, I go "Duuuuhhhhh... I'm a TREE."

I'll just end with this: it was at Green Bank that Frank Drake came up with his famous equation-that's-not-an-equation for estimating the probability of tech-capable extraterrestrial life. I've talked about it quite a lot in here; just do a search on the blog for "Drake Equation." This is really irrelevant to anything, but then, so is opposition to 5g.

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