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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September 17, 2023 at 8:28am

#1055859

Revisited: "Another Saturday Night"

Archaeologically excavating the bones of the midden heap that is my blog, we come to this early attempt at an entry from near the end of November, 2007: "Another Saturday Night"

The title comes from an old Cat Stevens song, but it was one of his more popular ones, so I guess I figured people knew the reference. That's the problem with reference jokes: not everyone is in on it. Though one could make the same observation about any joke that doesn't involve things we all share. Like farts. But fart jokes aren't funny.

I say all this because the whole entry was about me racking my brains for a Comedy newsletter editorial. I've done thirteen of those a year ever since the year I wrote that linked entry, and while it's sometimes easy to find a topic, I'm often stumped until the looming deadline forces me to just pick something, dammit. And not jokes about impending deadlines, either; that only worked once. Or maybe twice. I don't know; I'm certain I repeated many topics over the years.

Which reminds me, I need a Fantasy newsletter topic today. What will it be? I don't know yet; it's not close enough to the deadline for me to feel enough of a sense of dread, which is when my brain finally wakes up.

Anyway, from that entry:

Thing is, I didn't start out to be funny - I started out to write science fiction.

The two are, of course, not mutually exclusive, but one risks being accused of ripping off Hitchhiker's. Unless you're a Star Trek writer; they do a great job at jabs with Lower Decks.

A common trick in science fiction, one which goes all the way back to its roots in Mary Shelley's Frankenstein, is to write in the Alien Observer.

Ugh. The naïveté of youth. Half of this entry is embarrassing to me now, being so obvious. I guess it was new to me at the time.

So I won't paste more of that. I'll just note that, when I was done, I realized I had written myself into an editorial, assuming a few changes. It's been so long, though, that I don't remember if I actually used it or not, and can't be arsed to go back that far in the newsletter archives. It may have been the first time I turned a blog entry into a newsletter editorial, but it certainly wasn't the last.

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