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.

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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.

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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.

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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.

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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.

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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.

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April 30, 2023 at 3:38am

#1049023

Revisited: "Asking Persimmon"

Wrapping up another month in the relentless march to our individual and collective doom. As it is Sunday, I wanted to pull out a past entry and take another look at it.

As I've noted before, I don't take anything from the past year for revisiting. Today, though, cuts it pretty close; it's an entry from April 11 of last year: "Asking Persimmon"

Since it's so recent, not much has changed. The link, to an Atlas Obscura article, still works.

I made my perennial complaint about the inconsistency of labeling delicious fermented beverages:

In general, beer is fermented grain, while wine is fermented fruit. However, exceptions abound. Cider, usually from apples or pears, is its own category. Japanese sake is most often known as "rice wine" in English, probably because its alcohol content is higher than most beer and it's generally not bubbly. For example. So if someone wants to call this "persimmon beer," well, they don't need my permission.

Well, it's not a complaint, exactly. Just an observation. In the end, though, it doesn't matter all that much, as long as you pretty much know what you're drinking. That is, don't make a sparkling plum wine and call it peach beer. Or whatever. I had a mead yesterday that was also somehow categorized as beer because, it seems, there were grains somewhere in the brewing process. My understanding is that, to be called mead, most of its fermentation product has to come from honey—kind of like something has to be 51% de agave (and from a particular region) to be called tequila.

What I'm getting at is, as with many things such as mountains/hills and planets/dwarf planets, sometimes you run into a categorization issue. I'm mostly mentioning this stuff again because, from the article and my quote thereof, there's something that I apparently didn't bother talking about:

...fermenting Diospyros virginiana, the diminutive North American persimmon, with sugar, honey, and yeast...

So what I'm not real clear on is how much of the fermentation product is from persimmon, sugar, or honey. Persimmon seems to have enough sugars in it by itself for fermentation; I'd imagine the sugar and honey were about flavor. I highly doubt the ratio of those ingredients was consistent, though.

Probably doesn't matter. The story remains the same, and it's still just as interesting as it was last year when I linked it, or the year before when the article came out.

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