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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Show Recent Comments

10 Most Recent Blog Comments:

Wordsmitty ✍️

about an hour ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

1 Like

🌖 HuntersMoon

about 5 hours ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

1 Like

tj-Merry Mischief Maker

about 24 hours ago
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

a day 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

Dec 23, 2024 at 4:55pm
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

June 13, 2024 at 8:15am

#1072588

Curse-ive

Speaking of words, here's a list from Cracked:

11 Old-Timey Curse Words That Make You Sound Like Yosemite Sam
At the very least they might increase your ‘Scrabble’ score

Nowhere is the expression "words have power" more true than in the Land of Cuss. Cursington. Swearsburg. Naughtywordville. Whatever. But repetition makes almost any word lose its magic, until it becomes just another word.

That's why I think it's important to switch things up a bit, by making up new curses, or, as this article does, resurrecting old ones.

Even in my lifetime, the social acceptability of full-on sailor-mouth has become much more accepted.

My father would be offended by that description. He was a sailor, but rarely cussed. I guess he was trying to set a good example for me. Did it work? Shit, no.

I would have been hesitant to let loose a “damnit” around my parents in days of yore...

I once got upbraided by a Mennonite for saying "damn" in front of them. No, that's not how this works. How this works is: if you're around me, you put up with my curses. Because I do, in fact, give plenty of damns.

Now, like the headline says, there are 11 of these, and I can't be arsed to comment on all of them.

9 Gadzooks

You know a curse word has lost its power when it ends up as the name of a mall stalwart.

A what, now? Never heard of it.

A name that feels much grimmer once you realize that gadzooks is a bastardization of “God’s Hooks,” referring to the nails used to crucify Jesus.

You gotta wonder if that naming was on purpose.

If any mall store should have been called Gadzooks, it should have been Claire’s, given that they handled piercings.

There are two major classifications of naughty words: One celebrates and uplifts the most base subjects, like "shit" or the all-powerful F word. The other classification is blasphemous, like "goddammit" or "Christ on a crutch." This is why it's likely that the most perfect curse ever created is "holy fucking shit."

What's blasphemy to one religion, though, might be nothing to another. It's hard to blaspheme around me, for example, unless you try to tell me that my favorite beer is pisswater.

5 Rantallion

At first glance, you’d assume rantallion was a relative of “rapscallion,” but you’d be plum wrong. It’s a penis, but not just any penis: It’s a penis that's specifically shorter than the scrotum.

But what if you just happen to have low-hanging balls?

4 Quim

Quim is an antiquated synonym of a modern curse word, though it’s one that, at least in America, still gets you kicked out of a Panera Bread posthaste.

One of the most delightful things in any Marvel movie ever was when Loki got away with calling Natasha a "mewling quim" in a PG-13 movie. I mean, I knew what the word meant. Perhaps the MPAA did not.

1 Defenestrate

Okay, I'll admit, this isn’t a swear, but it is a delightfully antiquated word that everyone deserves to know.

Yeah, that's cheating. But it is a glorious word that deserves more popularity. As in, "The Mennonite threatened to defenestrate me for saying 'damn' in front of him."

3 Like • Comment • View 5 comments

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