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

September 20, 2022 at 12:01am

#1037901

On Sale

Today, we're back to talking about marketing. You won't believe what happens next!

15 Cultural Phenomena That Were Just Marketing Ploys

I'd argue that all of them are.

In the modern world, marketing pervades just about every aspect of our lives, from what we eat to how we spend our free time to who we rub our genitals on. Even some of the most basic facts of life and institutions we hold most sacred can be traced back to some guy who wanted to sell us something.

I've said before that science is value-neutral, but it can be used for good or evil. Marketing is an example of using the soft science of psychology for evil.

Well, okay, it's not always "evil." But I wouldn't call it "good" for anyone but the person making money and/or gaining power from it. So I think it's important to know the tricks, if only to protect yourself from it.

Since this is Cracked, the list counts down. And since there are 15 of them, I'm going to be choosy.

15. Coffee Breaks

...but it didn’t become widespread and wasn’t even called a “coffee break” until it reached the ears of the Pan American Coffee Bureau in 1952, when their launched their “Give Yourself a Coffee-Break” campaign to take advantage of the opportunity to sell more coffee.

No amount of marketing can convince me that coffee is something I should drink. On the other hand, Coke's marketing worked on me.

13. Bacon

Remember back in the 2000s, when everything from chewing gum to lube came in bacon? It was a confusing and chaotic time, and it was all because the health craze of the ‘80s plummeted pork sales, so executives crafted a backlash as a way to, again, sell more bacon.

On the other hand, bacon is delicious, and I've often wondered if Atkins was getting kickbacks from Big Pork.

Oh, and that decade was the noughties. Goddammit, I am going to make that a Thing. Even if I have to resort to marketing to do it.

11. Diamond Engagement Rings

I think people have finally caught on that this was a gigantic marketing gimmick by DeBeers, and yet the "tradition" (less than 100 years old, per this article) continues that one must gift slave carbon to one's betrothed.

10. Wedding Registries

By the 1920s, the ancient practice of showering newlyweds with weird symbolic gifts had mostly died out, and only their closest friends and family were expected to do anything more than party their faces off. That didn’t suit department store Marshall Fields, who invented the wedding registry in 1924 to sell more merchandise under the guise of providing the couple with everything they need to start their new life (except any kind of useful sex education).

Speaking of symbolic gifts, periodically, I'll see one of those "anniversary" lists that show what you're "supposed" to give each other for particular wedding anniversary milestones. I've wondered why more people didn't market based on that.

8. Father’s Day

Look, almost every holiday has been either co-opted by marketers, or came about specifically to sell shit. We know this. Father's Day is just one of the more recent of these. (To her credit, the lady who promoted Mother's Day

in the US was reportedly incensed about all the selling surrounding it.)

4. Ten Commandments Monuments

People are pretty protective over the monuments to the Ten Commandments that appear on government property across the country considering they didn’t exist until Cecil B. DeMille needed to promote a movie.

Worst of all, the vast majority of the Ten Commandments (whichever version you believe in) have absolutely no bearing on the modern legal system. But that's a blog for another time.

1. Santa Claus

Of course, Santa as we know him wasn't popularized until 1931, when Coca-Cola unveiled its latest holiday campaign featuring the red-coated, red-nosed, “huh, suspiciously red-focused” Santa of the modern era, inspired by the description in “‘Twas the Night Before Christmas.”

Perhaps one of the most successful marketing campaigns of all time, though I'm not sure how effective it is anymore at selling fizzy beverages. But considering I'm already seeing Santa-themed bullshit everywhere in September and I don't even leave the house, well, someone's making money somewhere.

And again, there's nothing wrong with wanting to sell something actually useful. It's only when that power is used for wicked ends, like overpriced fake-wellness products and chicken wings, that I have a problem.

1 Like • Comment • View 2 comments

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