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').

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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.

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

November 26, 2022 at 12:01am

#1041037

To Market, To Market

I've done entries about avocados before. Here are a couple: "The Devil's Avocat"

and "Another Avocado Article"

. This one's not about the fruit so much as it is about the product.

How Marketing Changed the Way We See Avocados
Once upon a time, Americans didn't know what to do with "alligator pears." Now we can't get enough

I have a confession to make: When I was a kid, I hated avocados. "Zaboca" as they are called in Trinidad (and maybe elsewhere in the Caribbean) were mushy and gross, in my young, uninformed opinion. They just didn’t taste like anything. Plus, I believed my parents ate some weird things in general.

I'm pretty sure all kids, from all cultures, have different approaches to food than adults. Hell, most of 'em probably don't like beer, even. But we usually grow up to actually like some of those yucky things mom and/or dad tried to shove down our gullets when we were little.

In the beginning of the 20th-century, they were called “alligator pears.” Their bumpy, olive skin connected them to those denizens of the swamp, and it’s shape resembled, well, a pear.

They had a marketing problem.

In addition to already discussing avocados, I've mentioned a few marketing problems in here before. Can't be arsed to find those entries, but I vaguely remember something about orange juice. And maybe chicken wings.

Along these lines, the California Avocado Grower’s Exchange launched a petition to change the name of the fruit, formally. They were pushing to get back to the cultural roots of avocados: The word “avocado” is derived from the Aztec “ahuacacuahatl.” This renaming was meant to further exoticize the product, lending credence to the idea that it was a special treat.

Another source puts it as āhuacatl. I don't know enough about the Aztec language to know if someone made a mistake or if maybe they used both words, or the one was a shortening of the other. Doesn't matter much, I suppose, but I do like to get these things right.

That was all well and good until nutrition experts began to promote a low-fat diet.

Wait, I thought that wasn't a thing until like the 1990s. Is this article skipping whole decades?

The public didn’t differentiate between saturated fats, which were target of this movement, and monounsaturated fats, which are “good” fats. Avocados came under fire.

Avocados under fire are disgusting. No, seriously, nothing's worse than a heated avocado.

So the avocado growers rallied. They funded research and put out studies meant to extoll the virtues of the fruit.

This. This is why people don't trust nutrition science.

The turning point for avocados was their integration with the [name of copyrighted sportsball game that takes place in Feburary redacted].

With enough money, anyone can advertise anything during that game and people will flock to it. If you put a halftime ad there selling boxes of unprocessed human shit, your shit supply would run out the next day.

The public’s investment and interest in the Su[bleep]wl cemented guacamole as a snack item, giving the avocado a foothold it needed. Access to avocados also increased as the previous ban on the import of this item was lifted in 1997, and fruits from Michoacan began to flow across the border.

Then why do I remember avocados from way back in the 70s? It's possible my memory is faulty, or maybe I shifted timelines.

At the end of the day, avocados have a place on today’s table thanks in part to a tireless campaign to redefine and redraft their identity. Some of it was misguided, some of it was weird and some of it was good. That is the nature of advertising.

I put up marketing articles here from time to time because many writers need to know how to do marketing. I mean, I would, but no matter how much I learn about it, I'm utterly incompetent at marketing (maybe because I won't pay for an ad spot during the game-that-shall-not-be-named). Doesn't stop me from reading about it, though.

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