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:

tj-Merry Mischief Maker

about 20 hours ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 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.

5 Like • Comment

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