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.

3 Like

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.

2 Like

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.

1 Like

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.

1 Like

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.

3 Like

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.

2 Like

August 31, 2024 at 8:37am

#1075949

Revisited: "Meet George Jetson"

In August and everything after
You get a little less than you expected somehow
—Counting Crows

I usually do these archaeological expeditions on Sundays, but, as I noted yesterday, all of next week will be (or at least should be) taken up by entries for "Blog Week Birthday Bastion 2024"

[13+].

The past, imperfect, goes all the way to April of 2007 today, for a short entry about consumer automation: "Meet George Jetson"

My wife wants a robot.

Yes, this was long enough ago that I was actually married.

No, not for that. I haven't been replaced by a machine yet. Or, well, maybe I have; her friends have been holding a lot of schtupperware parties lately.

"Schtup" is a Yiddish word for sexual intercourse. Her friends had these get-togethers where the host would demonstrate various "toys" (mostly made of plastic) and get some sort of commission on sales. It would have been impossible for me not to make a pun on Tupperware parties.

By "demonstrate," I don't mean what you're thinking. Get your mind out of the gutter, please.

But specifically, she wants a robot she saw that travels around the house, cleaning it.

A few years back, my housemate got a Roomba. It was a massive pain to organize around, since neither of us is naturally organized. There's barely enough open floor space for it to do its thing, and I can't be arsed to do all the work it would take to possess less stuff. It collects dust now, on top rather than inside.

Now, overlooking for the moment the years of therapy our cats will have to endure if we actually get this little slice of science fiction...

Also, the cats were not amused. Yes, I've seen those videos of cats sitting on the damn things while they scoot around, but my cats are different.

...glossing over the price (which, really, is probably comparable to an Oreck vacuum cleaner)...

The house is, and was, uncarpeted except for one single room. Not worth spending that kind of dough. Then I'd be the sucker instead of the vacuum cleaner.

...and even forgetting for the moment how this little gadget confirms my theory that if necessity is the mother of invention, laziness is the milkman...

Huh. I've been saying that for at least 17 years. I had no idea.

...aside from all that, there's something fundamentally wrong here:

There exists a household cleaning robot, and I still don't have my flying car.

Every time I complain that I don't have a flying car, two responses come soaring in, as if jerked by knees:

1) Flying cars do exist (generally accompanied by a link to a video);

2) People can't drive in 2D; imagine the chaos if they tried it in 3D.

For 1, I say "Okay, they exist. Fine. They're not production models and, more importantly, my complaint is not that they don't exist, but that I don't own one."

For 2, my response is that I don't give a good goddamn if anyone else has one; I'd be perfectly happy being the only owner of one.

I was promised a flying car. It was right there at the 1939 World's Fair: Flying Cars are the Future.

The far future, apparently.

Point is, how come she gets a household robot, and I'm still stuck driving a vehicle that never leaves the ground (except maybe when I'm being chased by Roscoe P. Coltrane)?

Spoiler: she didn't get a household robot. I'm not saying that the lack was a proximate cause of our divorce, but it probably didn't help.

There follows a link to a Popular Mechanics article (I presume from the URL), but the link doesn't work any more and I have no idea what point I was trying to make with it. Nor can I be arsed to search it out.

And just to forestall another assumption: it's not like I expected her to do all the cleaning. We both did that. Not that I would have done as much if I'd been single, as evidenced by the fact that these days, I hire a maid service, which is almost as much an organizational pain in the ass as the Roomba was.

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