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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

April 21, 2023 at 11:26am

#1048554

Boned

Oh good. If this prompt for "Journalistic Intentions"

[18+] hadn't come up at random, I might have had to write an extra entry.

boning

Ever boned a fish?

I haven't, because I don't fish, but I've seen people do it. And not on one of those websites, either. Seems like a lot of work, though as with anything, practice improves skill. Some fish just don't like to be boned, though, which can lead to oral discomfort or even penetration.

The word "deboning" in this context means the same thing, which is just one of those weird things about English, like flammable/inflammable or contronyms like "cleave."

But for this blogging activity, which is all about clothing, we're not talking about fish, or anything we do with our clothes (mostly) off. And for once, I don't have to do extensive research to know what it means.

Not fish, then. But whales, which live with fish but aren't them. Back before the inspired invention of the brassiere, for a while, corsets were all the rage. And back before plastics (see previous entry on nylon), corsets were stiffened by whale bones.

Which is oddly appropriate. See, "corset" comes from an old French word meaning "body." The modern version is "corps" (pronounced more like "core" just like with the Marine Corps, and not to be confused with "cœur," which translates to "heart" and is pronounced more like "curr," as in "no1curr") and from one of these we get the English "corpse." So you had people (it's associated with women's wear but for a long time all genders wore a kind of corset) wearing parts of whale corpses to support part of their own living bodies. An endoskeleton turned exoskeleton.

We (mostly) don't kill whales for fashion, or lighting, or meat, anymore. Instead, we use older corpses. Not of dinosaurs, per popular misconception and one oil company's brontosaurus logo, but ancient marine life. They're pumped out of wells, refined, and some of them get molded into plastic boning (yes, people still wear corsets; see any RenFaire).

Eventually, and not too far in the future, we'll run out of the corpses that took billions of years to accumulate.

And then, we're well and truly boned.

5 Like • Comment • View 4 comments

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