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

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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

August 27, 2023 at 9:40am

#1054708

Revisited: "Larry Flynt is a Better Man than I Am"

It's Wayback Day again, so let's see what the past has in store for us today.

Reaching deep into the bowels of the past, I plucked out something from May 16, 2007: "Larry Flynt is a Better Man than I Am."

This was so bloody long ago that it might as well be a different planet. The link in the article is, unsurprisingly, broken; I had to dig around a bit more for context, and the context is that Jerry Falwell had kicked the bucket the day before. I really should mark May 15 on my calendar as an annual day of rejoicing and merriment.

My mother told me never to speak ill of the dead, something ingrained in me from an early age, so yesterday's blog entry was rather difficult for me to write.

"Yesterday's blog entry" was a celebratory post announcing the death of that smarmy subhuman trash. At this point, I can't remember if it had actually been difficult for me to write, but I rarely outright lie in these entries; certainly, I've since overcome my reluctance to speak ill of the dead, if the deceased in question was a pox on the ass of society.

As for the title of the entry in question here, a quote from the now-defunct article, which in turn quotes pornographer Larry Flynt:

I hated everything he stood for, but after meeting him in person, years after the trial, Jerry Falwell and I became good friends. He would visit me in California and we would debate together on college campuses. I always appreciated his sincerity even though I knew what he was selling and he knew what I was selling.

Flynt himself bought the farm in early 2021, having outlived Falwell by well over a decade. I don't remember any obituaries about him at the time; I just now looked that up.

I wrote then:

And that's what it comes down to for me, folks. Whatever you may think of the porn industry, it doesn't try to hide behind some nebulous concept of greater good or try to justify its actions on shaky moral grounds. Lots of people want porn, and people like Flynt sell it. Period. Everyone involved, from the producers to the talent to the consumers, are completely aware, every step of the way, that it's all about selling the illusion of sex (or intimacy, as I would argue) in return for money. There's no "it's good for you;" there's no "buy our porn and all your sins will be forgiven."

Reading between the lines here, I think that was a statement against hypocrisy. While we're all hypocrites, and an examination of anyone's life or words will reveal contradictions, some hypocrisy is more blatant than others.

As I recall, that slimy fool's son was also caught in a massive hypocrisy a few years ago. Some sort of sex scandal involving pool boys or some such. Look, I honestly don't give a shit what antics you get up to in private, so long as everyone involved is, at least, consenting adults. But if you rail against extramarital sex and then turn around and indulge in it, the rest of us are absolutely right to call you out on it.

I should emphasize that none of this is actually meant to praise Larry Flynt, who did his own share of damage to the world. But my long-ago entry title stands: he was, at least in this instance, a better person than I was.

As for why I bothered with this in the first place, well, Lynchburg is only about an hour's drive from here, through some of the most beautiful countryside in Virginia. I have friends there, and, at the time, had even more. One of my friends there is in a same-sex marriage, which, again, I don't care—except to the extent that it would make Falwell spin in his grave. Attach a dynamo to it and you could power half of Lynchburg.

I think, though, my last line was a sick burn:

And if you want to know who was the better American, well... consider that Falwell's business never had to pay taxes.

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