Complex Numbers (Book)

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Complex Numbers

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/

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Show Recent Comments

10 Most Recent Blog Comments:

🌖 HuntersMoon

about 5 hours ago
In response to "With Pride"

I'm with you. ### (hashtag pound hastags)

1 Like

Elisa, Stik of Clubs

about 5 hours ago
In response to "Dis Dress Signal"

I think one type of disagreement that gets overlooked but could benefit from this approach is how to enact a shared goal (or express a shared value). Right now, so many disagreements in the spotlight are fairly basic (e.g. USAID should or should not exist). However, if we're going to form alliances to achieve a shared goal (e.g. provide a market for various crops to stabilize prices), we need to be mindful of differences in how these things get done. I worry that people not acknowledging differential priors will hobble potential (and necessary) alliances.

1 Like

Robert Waltz

a day ago
In response to "Dis Dress Signal"

tj wanderlust-words-in-motion

- Ah, but that's what they want you to think.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Dis Dress Signal"

Are you sure it's the lighting? I've heard the "dress" was a government scheme to divide the people and distract us from what's really important. It's all conspiracies, you know!

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Cerebral Musings"

I like to think of it as right brained and wrong brained, and many these days are wrong brained.

1 Like

tj wanderlust-words-in-motion

Feb 25, 2025 at 4:32pm
In response to "Solitary"

Having five brothers and one sister, I often seen less family stress in friends that were an only child.

1 Like

tj wanderlust-words-in-motion

Feb 24, 2025 at 6:17pm
In response to "Mystery"

#tiktokgirl: octothorpe, number, and as you indicated poundtiktokgirls. That's the problem with "the style these days", they distort all the coolness of the past styles.

1 Like

tj wanderlust-words-in-motion

Feb 23, 2025 at 4:32pm
In response to "Revisited: "Forgive Me, For I Have Zinned""

My oldest son, while in college, would buy it and mix it with Kool-Aid when he had friends over.

2 Like

Allan Charles 🐾

Feb 23, 2025 at 12:03pm
In response to "Revisited: "Forgive Me, For I Have Zinned""

I find White Zinfandel to be disgusting. Defining it as the wine equivalent to American cheese is a great comparison.

At my job, we only sold a cheap house wine for white zin, and when people ordered it I had to try to restrain my facial muscles from giving stank face.

2 Like

tj wanderlust-words-in-motion

Feb 22, 2025 at 7:36pm
In response to "Apparatus"

And then we have "cocktail" which can, if one takes the time to look it up, waste a good hour or more of time and provide various meanings and origins, including shoving ginger up a horses arse!

February 28, 2025 at 10:25am

#1084496

With Pride

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

#proudboys

As I've hinted in previous entries for JI, "pound" has several meanings. As a verb, it can mean to thump repeatedly, as in "go pound sand" or "his heart pounded in his chest as he ran from the angry mob." It can also mean to have dominant sex with, probably because of the similarity of that to the rhythmic thumping associated with the first verb version of "pound."

That's not even getting into the nouns, the ones for weight or currency (related to weight) or the place where they keep stray dogs (probably unrelated to weight and maybe related to "impound").

So when you say "pound proudboys," it's unclear whether we're supposed to lock them up with the other stray dogs, bone them, or punch them repeatedly into submission (and then maybe bone them).

I am, of course, not advocating for nonconsensual sexual relations; I'm strongly implying that, for them, it would be consensual.

Not that I'd volunteer, mind you. Even if I did swing that way, which I don't, I could think of much better uses for my time and energy. Still, they might have better luck in getting what they want if they named themselves Pride Boys.

And, hey, I'm not judging, or kink-shaming. That would be massively hypocritical, even for me. And it wouldn't be something to be proud of.

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