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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tj wanderlust-words-in-motion

about 20 hours ago
In response to "Solitary"

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

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tj wanderlust-words-in-motion

a day ago
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.

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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.

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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!

tj wanderlust-words-in-motion

Feb 21, 2025 at 3:02pm
In response to "Thwip"

Put it on ATVs so when they get stuck they can shoot out a web and winch themselves out.

2 Like

tj wanderlust-words-in-motion

Feb 20, 2025 at 6:10pm
In response to "One Fine Thing"

Well, it was a fine idea.

Adhere - Definitely Writing

Feb 20, 2025 at 7:48am
In response to "One Fine Thing"

I immediately thought of "Imfamy, imfamy, they've all got it imfamy." But then my mind does that.

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tj wanderlust-words-in-motion

Feb 19, 2025 at 3:59pm
In response to "Fail to Succeed"

In one way, it's good to have people with boneheaded ideas, it provides something to blog about.

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Adhere - Definitely Writing

Feb 19, 2025 at 1:36pm
In response to "Fail to Succeed"

Having drunk soda on both sides of the Atlantic, I have to say that Mountain Dew with HFCS in America tastes a lot better than the 'same' drink made with sugar here in the UK. The experience is smoother and so is the taste.

2 Like

February 26, 2025 at 9:04am

#1084400

Cerebral Musings

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

#brain

Not much I can say about "pound brain" except that, from what I hear, the brain itself doesn't contain pain receptors. So no matter how much you pound your brain, it's not the gray matter itself that hurts; it's the slightly harder stuff surrounding it.

Why you'd pound your brain is another issue, but, I mean... *gestures at everything in general* I get it.

My ex-wife had brain surgery. They took out a chunk of brain in an attempt to fix a neurological problem. This happened shortly before we separated. When I'm feeling charitable, I'll assume that the extracted bit was the bunch of neurons that made her fool herself into believing she liked being around me. When I'm not feeling charitable, I'll think that she had the surgery before the separation so that, in case something went wrong (as something sometimes does when someone goes digging around in a brain with surgical implements), I'd be on the hook to care for whatever was left of her.

The reality, of course, is probably something else entirely. Which is only fair, because whatever we think we know about the brain itself, we're probably wrong and definitely operating from incomplete information. And that makes it marvelous that we can even consider poking around in there with scalpels and forceps and whatnot, let alone doing so with any success.

For instance, there was this widespread belief that the two hemispheres of the brain ruled different aspects of one's personality. A "right-brained" person was, by this theory, creative, artistic, emotional, and so on. A "left-brained" person, in contrast, was considered logical, rational, methodical, etc.

Because people don't like to change their brains, this model persists in the popular imagination, but as it turns out, it's about as accurate as phrenology or astrology. Sure, some people are more creative and others, more methodical, but it has nothing to do with dominant cerebral hemispheres.

For another instance, there's a tendency to use metaphors to describe the brain's function. The latest involves comparing the brain to a computer, with different sections serving different functions like processing (CPU) or memory (hard drive). Before computers, it was fashionable to compare the brain to a machine; the image of cogs turning when someone is thinking persists in cartoons and whatnot.

These are more reflections of the current state of technology than of reality. But, like the Bohr orbital model of an atom, they can serve their purpose even though they're inaccurate.

So I say this: the brain is like a car. You don't have to know exactly how it works to use it, but a lot of people are really, really bad at doing so.

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