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

August 3, 2024 at 10:22am

#1074722

What a Pain

Among the destination priorities that I attempted to communicate to the travel agent were a few—just a few, mind you—places that don't involve fine fermented and/or distilled beverages.

Most of them are in Belgium, because my original 2020 travel plans were for that country. The list includes the Hergé museum (you know, the Tintin creator) and, just to balance things out, the Torture Museum

in Bruges.

This probably freaked her out, but hey, that's like 40% of the point. It's not like that sort of thing is unknown in Europe. There was an exhibit of old torture devices in a castle I visited once in Wales. That one took the edge off the horror by incorporating the kind of humor one expects from the Welsh (see also: Doctor Who). You know... dark and dry, like a fine porter ale.

When it comes to knowing how to inflict pain on other humans, humans excel at that shit. Oddly enough, it goes hand-in-clamp with empathy. The reason I say that is that in order to figure out what would cause other humans pain, one must have the imagination to put oneself in their (iron) shoes. Like, "Would that hurt? It would hurt me, so, yeah, I bet it would."

As far as I can tell, this sort of thing happened (and is still happening) all over the world, but perhaps because of our own cultural bias, the penchant of medieval Europe for creative infliction of pain, often for the most minor transgressions (or none at all), is very well-known. Pretty much everyone has heard of "The Rack" and maybe the "Iron Maiden" (whether the dungeon furniture is a worse torture than the band named after it is still an open question).

But it gets worse. Much, much worse.

From the Atlas Obscura article I linked up there:

It’s a wonderfully dark journey with tons of intriguing information. Many of the devices are equipped with mannequins displaying how they were used, which creates a lurid atmosphere.

Look, if anyone asks (the travel agent, for example), I'll just be like, "I'm a writer." Hell, that's my excuse for all my questionable Google searches.

The museum may be shocking to small children as there are wax figurines.

So don't bring your small children. Do I have to think of everything around here?

Best of all, if I go, I expect I'll be there in October. Perfect Halloween material.

1 Like • Comment

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