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.

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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 25, 2020 at 12:02am

#999073

The One Unforgivable Sin

I don't possess creativity.

PROMPT November 25th

Write about tinkering, brainstorming, or the process of creation. What brings out your creativity?

I know I've been over this before. Few things strike as much fear into my stony heart than the admonition to "Be creative!"

What I am is methodical and technical.

Now, I get that some people might question my self-assessment, what with my writing and all. But all I ever do is rearrange letters, words and concepts into something that's -- sometimes -- unique. What others might see in my stuff as creativity is more a result of randomness -- by which I mean, I literally pick things at random and then hammer them into some semblance of a form. Or, as with poems, the form exists and I just have to find the right words and rhythms and/or rhymes.

Having no creativity is, it seems, an unforgivable sin in our society. If I believed in such a thing as a soul, I'd say that the creative spark is the soul, and I never had one.

Take Legos, for example. Most people have played with Legos. Other people can take individual Legos and turn them into something new. Me? I have to follow the instructions or it becomes something indeterminate. You know in the first Lego movie where the entire theme was "don't freeze Lego creations into permanent form; be creative with them?" Well, that made it a horror movie for me. Everything is NOT awesome.

Or music, for another example. My attempts at making music sometimes followed the right form and structure, but there's no influx of creativity.

Fortunately, I went into a very technical, rules-oriented profession, where the soulless can, if not thrive, at least find a place. Hell, even my photography was more about the rules of composition, lighting, etc., than about any kind of artwork.

How, then, do I plan and plot a piece of writing?

Generally, I start at the end and work backwards. If I know, for example, that I need characters A and B to hook up at the end of the story, I can come up with plausible scenarios as to how they get together. If I'm working from a prompt, I find another prompt, usually through randomness, and combine the ideas. That's my theory on how writing works, by the way: not just one idea, but two or more, combined in what is hopefully a new way. If a single idea can be expressed in three ways, for example, when you get two of them together, you don't have six possibilities but nine. The more ideas, and the more ways in which they can be expressed, and the possibilities become, not infinite, but large enough as not to matter. Like shuffling a deck of cards: it's unlikely that any particular arrangement of a thoroughly shuffled deck of cards has ever been made before in the entire history of cards.

I try to find through-lines. It's an old design trick, to repeat a certain theme in different ways. A particular necklace, or the concept of "necklace," for example, can take on a different meaning in different parts of the story.

Mostly, though, I just write. When I feel stuck, I freewrite. This usually helps shake something loose, just vomiting ideas onto a screen.

The thing about technical stuff is, these are things that can be taught, learned, improved. Creativity isn't learnable. You either have it or you don't. It's kind of like how some people are born blind or deaf: they can get along just fine, and they even have the advantage that no one is going to judge them for their missing sense, the way they judge the uncreative.

I can admire creativity when I see it, though when it's not paired with technical skill I'm generally not impressed. I'm also not impressed when a bunch of people get together and try to out-create each other, like at Burning Man. Want to impress me? Have the courage to change the name to Burning Woman and deal with the inevitable backlash.

At this, I got curious about this year's Burning Man, something I've never been curious about before. Usually stuff about it is background noise for me when I'm looking for interesting stuff on the internet in the summer, but I just realized I didn't hear word one about it this year. Obviously there's good reason for that, but I didn't even notice its lack until just now. Turns out the festival was all-virtual this year.

I bet they got creative with it.

I don't care.

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