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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October 6, 2023 at 8:45am

#1056859

Plum

Plum
an entry for "Journalistic Intentions"

[18+]

Ever prune a plum tree?

One of the many linguistic confusions that plagued me as a kid—alongside such old standbys as flammable/inflammable and the various pronunciations of -ough—was a result of us possessing a plum tree.

We had lots of fruit and nut trees. A miniature almond orchard adorned our front lawn; the garden was peppered with walnuts. Off to the side stood several fruit trees, including apple, peach, cherry, and plum.

All of those fruits are somehow used to connote something good or desirable. For instance, my father claimed I was the apple of his eye, at least until I did something bad (which was, of course, a regular occurrence, at which point he would pare me, and not spare the rod). When things are going well, people say they're "peachy" (but they also say that when everything's going to the pits, because people love sarcasm). A really nice thing can be "cherry," and, of course, a particularly great job is a plum assignment.

You know what's not a plum assignment? Picking fruit and nuts off of trees. My dad was too old to be climbing trees, and there were a couple of years in there between "too young to climb trees" and "too teen to care about anything."

But all of these trees, and others, needed to be pruned on a regular basis, and that's what caused me the greatest confusion.

Because a dried plum is called a prune.

Now, I heard it through the grapevine (we had one of those, too) that those words, plum and prune, are linguistically equivalent, unlike, say, grape and raisin. And there's no special word for dried cherries; they're just dried cherries. The botanical binomial for the various species of plum trees starts with prunus, which is obviously where we get prune (dried plum), but not prune (the verb), which, through a tidal wave of linguistic gymnastics, also traces its origin back to Latin... but this time, from the word "rotundus," which, if you've been paying attention, obviously means "round." I guess it came from the practice of making trees look round, like a kid would draw? I don't know. Contrary to popular belief (which I foster), I don't know everything.

None of which explains how we got "prune" from "rotundus." The more recent etymological ancestor, according to the online dictionary I just looked at, is an Old French word: prooiginier, which I guess I can see.

All of which is to say it has nothing to do with plumb, plumber, or plumbed, which comes from the Latin word for lead. The metal.

If this is confusing, well, good. Welcome to my world.

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