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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June 11, 2023 at 9:57am

#1050930

Revisited: "Amazon"

Today is Throwback Day, and the random number generator pointed me to this short entry from October of 2018: "Amazon"

It really is incredibly short, but I still have a few things to say.

Upon looking at my Amazon account today, I saw:

"Customer since 1997."

It was a better internet all around back then. Except for the relative lack of streaming video. I was in my "no TV" phase, because broadcast TV was crap, and I flat-out refused to pay for cable. "Wait, you want me to pay you and still have to watch idiotic commercials? No."

That's right. My Amazon account is now old enough to drink.

Obviously, it's even older now. Old enough to drink more due to disillusionment with life.

Which is ironic, because Drunk Me keeps buying surprises from Amazon for Sober Me, like Doctor Who boxed sets (complete with sonic screwdriver) and lame Halloween costumes. And, once, a breathalyzer.

That doesn't happen as much anymore. Not even during the pandemic. Not because I didn't get blitzed, but because Amazon has become difficult enough to figure out when sober, and almost impossible when you're reeling from that seventh shot of tequila.

Like, you go and search something simple, like, I don't know, Star Trek bedsheets. You'd expect, when searching for that particular three-word phrase, that it would bounce back a list of Star Trek-themed bed linens. But no. First you're confronted with Sponsored Items that have nothing to do with Star Trek, or sheets. Star Wars shower curtains. PVC plumbing supplies. DVD boxed sets of Survivor. Glitter-infused dildos. Electric drills. Psychedelic pencils. And then, after the barrage of ads, you still get the same eclectic mix of irrelevant (to the search terms) crap, with maybe, three pages in, one solitary offering of Star Trek bedsheets. For a single-sized bed. Which I suppose is fair.

I didn't actually search for Star Trek bedsheets while preparing this entry, so I don't know if those particular items come up. I don't want that in my "suggested items" list for the next ten years. It would be different stuff depending on what you've searched for before, which is fine; if you're going to give me ads, at least give me targeted ones. But my point is, there's a whole lot of irrelevant stuff, most of which don't actually have their names in their titles but search engine terms, like, I don't know, Home Generator Maintenance Supplies Maintenance Supplies for Home Generator Electrical Mechanical Bolts Nuts Replacement Parts Oil Pan Drain Plugs.

I really should get an ignition interlock breathalyzer for Amazon. I guess I haven't been drunk enough to do that yet.

Turns out I didn't have to, because Amazon has made it virtually impossible to browse drunk.

And I'm not even going to get into the other issues with the company. I'm only talking about the site's user interface, here.

I still use them, because if there's anything I hate worse than ads, it's shopping in an actual store in an actual building. But damn, I miss the days when it was just a bookstore.

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