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

November 8, 2020 at 12:04am

#997877

Adventure Time

I'm not sure I've ever been on what one might define as an "adventure."

PROMPT November 8th

Tell us about the most memorable adventure you've ever been on. Did everything go according to plan, or did anything unexpected happen?

Also, if everything goes according to plan, I'm pretty sure it doesn't qualify as an adventure.

Sigh. I guess I'm going to have to resort to the dictionary again.

adventure (n) an unusual and exciting, typically hazardous, experience or activity.

I mean, it's not like I've trekked across Antarctica or braved the Sahara or rowed across the Atlantic or shit like that. Nor will I, at least not willingly.

I could, I suppose, talk about the time I went horseback riding through a Central American rainforest. Or the week I spent at 10,000 feet in the Rockies. Or the time I attempted to learn scuba diving off of St. Thomas only to be betrayed by my eustachian tubes. Or the times I managed to not get shot by jealous husbands / boyfriends.

There was also my first cross-country trip, which I mentioned in here fairly recently. Like, all the way back in July. Here: "The Not-Shining"

I'd say that was unusual, somewhat exciting, mildly hazardous, and both an experience and an activity. And memorable too.

Or one time on a different cross-country trip, I stayed at the Clown Motel in Tonopah, Nevada. Why do I mention this? Well, just to freak out anyone with coulrophobia, of course. The worst danger I ran into there, though, wasn't the clowns, or the ghosts that are supposed to be haunting the place, but a wonky room heater because Tonopah gets awfully damn cold in the winter.

I've walked around New York City at night, navigated back roads in Iowa, drunk beer at a biker bar in Montana, driven through a blizzard in New Mexico, gotten pulled over for speeding in Texas, and visited an active volcano in the Caribbean.

There's more, but since I can't think of them right now, I guess they don't count as "memorable."

So I guess what I have to say is there's only been one "most memorable adventure" for me, one that's had its share of hazards, excitement, and a great deal of the unexpected.

By which, of course, I mean life.

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