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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QPdoll

about 15 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

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Wordsmitty ✍️

about 18 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

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Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

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Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

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Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

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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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