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 15, 2020 at 12:01am

#998384

Good Enough

Well, this is a trick question.

PROMPT November 15th

What does “a good life” mean to you?

The reason it's a trick question is that "good" has too many definitions.

It can indicate a desirable state: good news, good quality, a good road, etc.

It can demonstrate a subjective opinion: a good movie or book, good food, whatever.

It's a moral judgement: she's a good person, he does good deeds.

It describes an emotional or physical state: she feels good, he looks good, a good time.

It indicates skill: he's good at writing, she's a good painter.

It's a simple compliment: You're a good kitty. (I say this a lot even when it's not strictly true.)

And there's probably more, including the (mis)use of it as an adverb, substituting for "well," as in "You cook really good."

French is no help in this regard, by the way. You can translate "good" into several different words, and I'm rarely sure when to use, say, "bon" and when to use "bel." I may never figure it out, but someone's got to annoy the French and it might as well be me.

So asking me what "a good life" means depends entirely on context. Are we speaking ethically or materially? Is it a matter of something that happens to you or something that you have to work for?

Change the article in the phrase and you also change the connotation: "a good life" can mean something different from "the good life." Une bonne vie, la belle vie.

Fortunately, as a writer, such ambiguity is a benefit, although I haven't delved into it until right now so my thoughts aren't fully formed. But if I were to plan out a story entitled "A Good Life," I might contrast the life of someone dedicating their actions to helping others, and someone living a life of leisure and luxury (which, contrary to popular belief, does not preclude also helping others). In other words, one living to do things for others, and the other living for the pleasure of it. I'd want to show, in such a story, that both individuals are pursuing their own idea of pleasure, though Other People are going to hold the first person in higher regard than the second... which is, of course, selfish on the part of Other People because they're the ones benefiting from it.

Put another way, Person A pursues charity and derives pleasure from helping others, while Person B pursues comfort and derives pleasure from leisure. (You, uh, should read that last phrase in a British accent for best effect.) We say that Person B is selfish, but the only real difference between them is the actions they do to satisfy themselves -- and how those actions are perceived by others.

Honestly, I'd choose a mix of both -- like I said, they are not mutually exclusive, though in our binary-loving society people tend to think in extremes and exclude the middle. I've noted before the false dichotomy in the sentence: "It is better to be poor and happy than rich and unhappy." ("Better," you'll note, is the comparative form of "good.") It is a false dichotomy because a) it's possible to be poor and unhappy; b) it's possible to be rich and happy and c) from the original choices, I'd personally rather be rich and unhappy.

But, if I were forced to pick from one or the other, I'd choose "a good life" as in a life of comfort, luxury, travel, gourmet food, expensive scotch, delicious beer, and all the finer things. That's good enough for me. Those who don't see that this also helps other people along the way might benefit from a good course in economics.

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