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:

tj-Merry Mischief Maker

about 14 hours ago
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

about 18 hours 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?

3 Like

🌖 HuntersMoon

about 21 hours ago
In response to "Gray Matters"

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

2 Like

tj-Merry Mischief Maker

a day 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

Dec 24, 2024 at 5:16pm
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

May 17, 2024 at 10:59am

#1071264

Mincing Around

Looks like someone gave Cracked a makeover. The most obvious change is that their logo no longer resembles that of the second-rate Mad ripoff they started out as. Not changed: countdown lists.

5 Words We Only Use Because the Old Ones Were Too Dirty
People only started talking about light meat and dark meat because they were too embarrassed to talk about breasts and legs

Yeah, and now "light meat" and "dark meat" have sexual connotations, because humans can be assholes. (When I was a kid, they called it "white meat," which I suppose comes with its own dark connotations.)

A friend is getting married, and you open up their gift registry. You see a “Dutch oven” listed there, and you suppress a giggle.

No, I don't, because 1) All my friends are past the "gift registry" stage and 2) I don't find the dirty version amusing in the slightest.

Later, at the ceremony, you deliver the toast, and you mention your Dutch oven observation. This angers and confuses people, who have no idea what you’re talking about. You are expelled from the venue.

As some people here can attest, my wedding toasts are simultaneously funnier and more cringeworthy than that.

5 Light Meat and Dark Meat

Light meat and dark meat are two different kinds of flesh on a bird. Confusingly, these names have nothing at all to do with white meat and red meat — all poultry is white meat, but some is light while some is dark.

And yet, we manage to infer the intended meaning from context.

Dark meat is fattier than light meat and arguably tastier.

Not to me. You could say I'm a breast guy.

But today, “light meat” and “dark meat” also sound sexual, so let’s just say whatever’s easiest.

Like I said.

4 Rooster

If we’re talking chicken double entendres, we of course need to talk about cocks. The cock is the male chicken, otherwise known as a rooster.

Honestly, this one's so obvious, I feel like the author got lazy.

3 Missus

The title in front of your name may reveal your gender, marital status, profession or level of nobility. The most common one for men is Mr., while women have Mrs., Miss and Ms. “Mr.” is short for mister. “Miss” isn’t short for anything. “Ms.” is pronounced miz but doesn’t represent any word other than “Ms.” itself. As for “Mrs.,” that’s pronounced missus of course.

And don't get me started on how some women take serious offense at being called "ma'am." In the US, this seems to be a North vs. South thing, though it's unlikely to start another Civil War. No, we have other things that will cause that.

2 Canola Oil

A lot of our vegetable oil comes from a plant named Brassica napus. The common name for this plant is rapeseed, with the “rape” part deriving from Latin word for turnip.

I'm almost sure I've written about this before, but I'm not about to put "rape" into the search box to verify.

1 Rabbit

Rabbits used to be called “coneys.” You’ll know that if you’re a fan of Lord of the Rings, in which Sam assures us that cooking a rabbit in a stew is the “one way to eat a brace of coneys.” He pronounces the word “cone-y,” the same way we pronounce Coney Island today, but originally, this word was pronounced “cunny.”

In the 16th century, “coney” became a pet name for women. Meanwhile, people already had the Latin word cunnus for “vulva,” which also gave rise to such words as cunnilingus and...

...couldn't they find a way to do this without typing the next word?

(Look, there's no reason why I can't say "cunt" once in an entry, but the opportunity to make the "couldn't" pun was overwhelming to me.)

Anyway, this is similar to why we don't call cats "pussy" anymore, except to set up or follow through with jokes. For example, long ago, Zsa Zsa Gabors was on The Tonight Show, way back in its heyday when Johnny Carson hosted. She came in with a cat, which perched on her lap.

Gabor: "Would you like to pet my pussy?"

Carson: "I'd love to, but you'll have to remove that damn cat."

...well, actually, that never happened.

But it's still funny.

3 Like • Comment

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