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

1 Like

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

October 6, 2021 at 12:02am

#1018774

Evil Genius

Corporations do some shady shit sometimes, but corporations, like Soylent Green, are made of people, so that should be no surprise.

5 Business Tricks That Were So Devilish, We Ain't Even Mad

In general, companies are evil and do all kinds of antisocial nonsense. But some tactics don't fill us with rage. They leave us wanting to clap the company on the back, saying, "You son of a gun, I wish I thought of that."

Link is from Cracked, so of course it's a reverse numbered list.

5. Nathan's Hot Dogs Dressed Customers As Fake Doctors To Make The Food Look Healthy

No one buys hot dogs because they're good for you. We buy them because fat and salt are delicious, as though ground lips and anuses are the tastiest pasts of the animal.

Hey, credit where it's due:

"You know what they make those things out of, Chet? You know? Lips and assholes!" I had to look it up, but it's from a movie called The Great Outdoors, from 1988, and it was a Dan Aykroyd line. Never saw the movie. Been quoting it for decades.

In the end, the cheaper dogs did win out, and this was helped by Nathan's scheme to make the meat look safe. He planted some customers at the stand wearing white coats, and also photographed some of these very scientific-looking men for promotional photos. He never actually said these were doctors, so he didn't commit fraud. But customers assumed these were staff from the nearby Coney Island Hospital, and if the dogs were good enough for the doctors, they couldn't be that bad after all.

Wouldn't be the last time, either. Us old folks will remember the ad: "I'm not a doctor, but I play one on TV."

4. A Vodka Company Created A Whole Bank

Roustam Tariko made his first fortune importing a restricted product into Russia and breaking protocol by selling at stores anyone could access. This product was Ferrero Rocher chocolates. He moved on to importing alcohol then created Russia's first own premium vodka brand. Vodka had always been popular in Russia of course, but up till this point, we guess people just made vodka from rotting potato peels, as anything more extravagant was previously banned under communism.

Almost every story I see about Russian people -- not the government, mind you, but the people -- involves two things: 1) vodka and 2) a badass. I have to think that's not a coincidence.

Incidentally, there's a popular misconception that vodka is made from potatoes. It can be, but you can make it from any starch or sugar. Consequently, you make it from whatever's cheapest. Like, maybe, rotting potato peels.

When Tariko's new Russian Standard vodka debuted in 1998, it was a huge success.

I should also note that, while I'm not a vodka snob the way I am with other booze, I always buy Russian Standard. It's just that good. But that's not the important part of the story. You'll have to go to the link to get the details, but basically, he found a remarkably clever way around Russia's various bans on advertising alcohol.

3. The "I Don't Care" Phone Company Grabbed Customers Who Didn't Care

Kids these days will simply not comprehend this entry. Hell, I barely remember those dark times when different communications companies were competing for long-distance call revenue.

2. The Case Of 1-800-OPERATER

More dark stories of a dark time. At least hot dogs and vodka are still around. (I don't eat hot dogs anymore, by the way; I can't get the lips and assholes line out of my head whenever I see one. Even beef ones.)

1. Home Depot Filled Itself With Prop Merchandise

Again, best to read the actual article so I don't fill this up with quotes. But I gotta say, this one was genius. Pure, evil genius.

I don't shop at Home Despot, either.

Now, if only I could come up with a sinister yet legal plan to part rich people from their money and transfer it to me...

I'd never seen the first Venom movie. Much as I like comics-based movies, I've never been a big fan of the Venom character. But I wanted to see the sequel, which meant renting the original first so I wasn't going into a sequel completely unprepared. I liked the first one well enough once it got the momentum going, but this isn't about the first movie; it's about the second. So.

One-Sentence Movie Review: Venom: Let There Be Carnage

Don't expect high art here; this movie is a CGI slugfest, and if that's your expectation going in, you probably won't be disappointed -- though you should definitely see the first movie before doing so, or it will make even less sense than it already does.

Rating: 3.5/5

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