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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10 Most Recent Blog Comments:

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').

1 Like

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

1 Like

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 7, 2024 at 10:11am

#1074867

I Kid You Not

Let's get this out of the way up front: I don't hate kids. There's this persistent binary belief that you either have to love something or hate it, and there's no range in between. I also don't hate dogs; I just don't want to own one or be in a place where someone's biting my ankles. So this Lifehacker article appealed to me, despite the source.

The Best Places to Go When You Don't Want to Be Around Kids
You don’t have kids, and you don’t want to hang out with kids. Here’s how to find places to live, vacation, and go out where you’re guaranteed to be child free.

Besides, would you trust a single, childfree dude in his 50s who says he "loves" kids? I didn't think so.

There are a lot of reasons someone might choose to be child free, either for a short time or permanently. Some folks just don’t have any desire to be parents, some can’t afford to be parents, and some parents just need a break from their kids from time to time (which is totally normal and okay).

"I just don't want to" should be a more acceptable answer to "Why don't you do [something]?"

Of course, just because you’re not bringing any kids doesn’t mean other people won’t. Some folks seem to believe that children should be welcome everywhere, in every situation, no matter what.

And that's the other part of it: it's usually not the children who are to blame; they're basically AI being trained on a data set. It's the parents who ought to know better.

Whatever the reason, you can’t always guarantee you’ll have a child-free experience—unless you plan ahead and choose your destinations wisely.

Well, I'm purposely going to Europe in the fall, when most kids are stuck in school. And my primary interest involves various forms of alcohol. This doesn't stop parents from showing up with their little accessories, but it does cut down on the volume involved.

So, where are these magical places, these anti-Disneylands, according to Lifehacker?

55+ communities

Yeah, no, I'd have to learn how to play golf.

Child-free resorts and cruises

Maybe as a last resort. (Damn right pun intended)

And if you’re looking for a really adult resort, you can seek out “sex-positive” vacation spots where you can let it all hang out.

Hard pass. See, this is my problem with everything in general: "Adult" shouldn't necessarily imply sex. Sometimes you just want to chill with people who talk about something other than Bluey, or whatever the kids are into these days.

Restaurants

If you’re just looking for a night out without dealing with screaming kids or misbehaving pre-teens, finding an adults-only restaurant is just the ticket. While many restaurants aren’t specifically no-kids-allowed, there’s a growing trend of restaurants advertising themselves as “adults-only,” promising a dining experience free of chicken fingers and the buzz of multiple screens designed to (hopefully) keep youngsters occupied while the adults attempt to have a conversation.

I've mentioned at least one of them in here before, I'm sure. But it's not too difficult to just avoid any restaurant with the word "family" in its name or description.

Spas

I'm not really in their demographic, either.

Lame list, after all. Let me tell you how I avoid kids:

Travel alone.

Airline upgrades (you can barely hear the wailing from up there in first class).

Bars, especially dingy dive bars.

Wineries. I'd say breweries, but many of them are family-friendly by design. Which doesn't stop me from going there, of course.

Cigar lounges. For obvious reasons.

Casinos. Occasionally, you'll see some harried parents rushing their kids through the casino aisle, but the draw of a casino isn't the gambling; it's that anyone under 21 is generally prohibited.

Thing is, though, it's not like I build my life around avoiding kids. The misbehaving ones, sure, but that risk is minimized by going to less family-oriented places and/or going somewhere (like a beach, say) during school months. I dislike dense crowds in general, whether or not kids are involved.

In short, this list sucks and was obviously put together on a short deadline.

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