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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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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October 29, 2021 at 12:02am

#1020340

Squash Court

Final entry for November's "Journalistic Intentions"

[18+]

Delicata Squash

One bit of trivia I remember from my misspent youth: "The pumpkin is the only edible gourd."

Like much of the trivia foisted upon an impressionable child, it's false... though the definitions of "pumpkin," "edible," and "gourd" are as squishy as a jack-o'lantern on November 1.

Botanically, cucurbita pepo (which if you follow the link would be the binomial for, among other vegetables, delicata squash) is interesting, similar in some ways to citrus fruits or the cruciferous vegetables cabbage/kale/broccoli/cauliflower/kohlrabi/etc. Or dogs, for that matter, though "botany" and "dog" don't really work together. The point being that for some species, innate genetic traits make diversification relatively easy.

Based solely on the Wikipedia article linked above, Delicata squash is a cultivar of the same species that also yields such diverse foods as zucchini and spaghetti squash... as well as some varieties of pumpkins. The reason the definition of "pumpkin" is squishy is that, just to cloud the matter, some pumpkins are of an entirely different lineage.

The reason the definition of "edible" is squishy is that for a long time, I didn't consider zucchini to be edible. Lately I've grown rather more fond of it, when properly prepared (it took a long time to get over my mother's cooking habits). But it obviously tastes quite different from pumpkin, and apparently also from delicata, which I haven't actually tried.

And the definition of "gourd" is squishy because... well, that gets into a lot of details that are irrelevant to the discussion at hand; basically, gourds were known in Eurasia/Africa from antiquity - they're even mentioned in the Bible - whereas seeds taken in prehistoric times to the American continents took a different path, one which brought us to pumpkins and squash like zucchini. Which, to muddy the waters even further, is known as courgette in the UK and France.

That's right -- despite the obvious Italian origins of the name, zucchini is (or to be pedantic, "are") American. By which I mean the continents in general, not specifically from the US. This origin, they share with things like tomatoes, potatoes, and maize, all of which Europeans happily adopted in an early bout of cultural appropriation.

Anyway, despite its relationship with pumpkins, I don't think anyone's going to carve delicata squash for Halloween. But it sounds to me like a good addition to any harvest feast.

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