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').

1 Like

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

1 Like

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

December 11, 2020 at 12:01am

#1000033

Ring Out

"30-Day Blogging Challenge ON HIATUS" [13+]:
11. National Noodle Ring Day
This is not just some random food holiday about pasta forming a ring. It is about a special dish everyone can cook who has a bundt pan and noodles. The noodles have to be cooked and then filled into the bundt pan. Anything can be added now: from eggs, tomatoes, cheese, carrots, or bacon, and of course the sauce. The dish now has to bake and can later be turned upside down.
Thought and opinions? Something you might try?

"JAFBG" [XGC]:
Some say this is the time of year to make peace. What are you coming to terms with as 2020 draws to an end?

No.

To both.

The former reminds me too much of the gelatin molds that were inexplicably popular when I was a kid. Look, I'm sure the noodle ring can be delicious -- how could it not be; it's pasta -- but I have better things to do with pasta, and if I'm going to bake it, it's going to be in a normal pan because I don't do "cute."

We all like different things for different reasons, and I made peace with that a long time ago -- at least in culinary matters. As for the kind of peace the other prompt is talking about, of course I'm for "peace." On earth, goodwill to humanity, etc. Nothing wrong with that. It's just the whole "coming to terms with" I'm not going to go out of my way to do.

Eventually we either make peace with whatever bad stuff happens, or we die first. No need to rush it, especially when there was so much about this year that was just insufferably bad for so many people. It's easier for me knowing that shit's basically random. Other people, I know, take comfort in believing that it's all part of a plan. But other people would probably also make and eat Noodle Rings. Whatever.

Yeah, I know I usually have more to say in here, but nothing important happened yesterday and the prompts really aren't inspiring anything. I mean, food prompts usually at least make me hungry, but not this one. Tomorrow, though... probably then I'll have something better to say.

7 Like • Comment • View 2 comments

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