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.

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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 13, 2021 at 12:03am

#1021510

Procreation Pass

Oh man, I thought I had that first draft of a story set on private.

PROMPT November 13^th

A Science-Fiction type prompt tonight. In your world, all citizens are temporarily neutered at birth. When you want to become a parent, you must prove to the government that you’ll be suitable caretakers and providers before you are allowed to procreate. How do you 'prove to the government' that you'll be a good caretaker/parent.

Oh, yeah, it is set on private. But I can't have been the only person to think of this, because...

This is an excellent idea.

I have long thought that one of life's great injustices is that in order to adopt a child, prospective parents have to jump through all sorts of fiery hoops, balance on a tightrope across a pool of smoking acid, and juggle chainsaws. Meanwhile, any two idiots can (and often do) get together and procreate with impunity.

There are at least two ways to fix this. One, just let anyone adopt who wants to. Yes, this risks people adopting kids for nefarious purposes, but as there are biological parents who use their offspring for nefarious purposes, I don't think this is a good argument against it. Two, go the other direction and make everyone who wants kids do the circus act.

There are certainly other solutions, but for the sake of (relative) brevity here, I won't consider them; the prompt goes with option 2. This would, in theory, ensure that everyone who raises a kid has some minimum qualifications for the job, just like any job has certain minimum qualifications. Result: happier, healthier, better-adjusted population. It would be utopian.

Like I said, in theory.

Because...

This is a horrible idea.

In reality, such a system would be rife with corruption.

Around the time when I was born, there was really only one way to adopt a child, which was to go through an adoption agency. Those agencies would vet potential parents and make the decision for them. All of the adoption agencies in the US were Christian, and so they only placed kids with Christian families. My parents, being Jewish, had to do an end run around this to get me.

Religious discrimination is only one of many ways the system would fail. There would be racism, too. And if whoever's making those decisions doesn't like homosexuality, then gay couples would never be able to adopt or even make arrangements to procreate. There is scientifically no way to design a fair system of deciding who is and is not allowed to have kids. Want to make sure they're well provided for? Discriminates against poor people. Want to have only the most intelligent people reproducing? Well, that's eugenics, and we all know how that works out.

Whoever is in power would use the system to punish anyone who doesn't fall in line. That's just the way politics works. Wrote something criticizing the government? No Procreation Pass for you. Participated in a strike against your employer? We only want citizens who are willing to work for low pay, so rejected. Have that one social media post where you got drunk and peed on a cop car? Sexual deviancy; no kids for you.

No, it would be dystopian.

The closest thing to a perfect system would be to find a way to ensure that anyone who wants a kid gets one, and anyone who doesn't, doesn't get saddled with any. No more accidents.

I mean, if you're talking science fiction, I could see something like the setup in the prompt happening on a temporary basis, say on a generation ship where resources are limited and tightly controlled. It would still end up causing conflict. Which is great for stories, but not so wonderful in real life.

But that doesn't address the prompt.

"How do you 'prove to the government' that you'll be a good caretaker/parent."

Answer: I don't. I never wanted kids.

But if I did, I'd demonstrate that I'm not abusive, that I'm stable, and that I have the means and ability to care for a larval human.

However, I can demonstrate all these things in real life — I've been able to do that for a while — and I still don't want kids. It's not like there's a shortage of them right now.

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