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

January 4, 2021 at 12:01am

#1001372

Irritation

PROMPT January 4th

Start your entry with this statement: “I am frustrated about ________ because ________.”

I am frustrated about health insurance because I don't know if I have it or not.

I think I wrote about some of this last month, but the quick recap is this: I have been getting mixed messages from my health insurance company about whether the new policy, which should have started January 1, is in force or not. They sent me a card, and the website says I'm insured, but they also kept sending me notices that I had to choose a plan (after I chose a plan), and the automatic payment which always posts on the first day of every month has not shown up on my bank's online records yet.

Welcome to America.

And naturally, I haven't been able to contact them because Friday was a holiday and they don't take calls on weekends.

Later today, I have a routine doctor appointment -- one to which I do not wish to go if I don't have a plan in place, for reasons that Americans might understand but would be incomprehensible to folks from civilized countries.

And if it turns out that by not having paid them on the first, they've canceled any plan I might have in place, I'll probably end up without health insurance for the rest of the year.

During a global pandemic.

Now... probably... everything will be fine and they'll suck up my money later today and I'll be insured this year. I just wish they could have been more clear last month, when it was possible for me to do something else about it. I called them twice toward the end of the year, and both times they're like "everything's fine, you'll be insured, the premiums will get charged automatically on the first of the month."

Well, since that didn't happen, it's... like I said... frustrating. It also makes me wonder what else they're being unclear about. "Oh, we don't cover anything that actually happens to you. Money flows from you to us, you know, not from us to the doctors."

I'm not trying to get political here, and I don't mind paying a reasonable amount for medical services. It's just that my definition of "reasonable amount" isn't $12,000 for a band-aid and a dab of Neosporin. I live two miles away from one of the best hospitals in the country, but what good does that do when I can't afford their services?

It's difficult for me to believe that I'm the only person in such a situation, either.

While we're on the subject of frustrations, though, have you ever put on an article of clothing only for something on it to poke you? Like, just some kind of small, hard fiber that irritates your skin. And then when you go looking for whatever it is, you can't find it? So you rearrange your clothes, but pretty soon they fall back into place and the thing is scratching at your skin again?

Well, that's been happening to me all weekend and it's making me meshuggah.

Still, that's pretty minor compared to the health insurance thing. But it's not helping my mood, either.

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