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 2, 2024 at 11:19am

#1070406

Butt Of Course

As luck would have it, we get another Cracked link today. I don't really know why I saved this to my queue other than thinking, "You know what my blog needs more of? Juvenile cringe humor."

5 Horrible Things That Happened to People’s Butts

These are, of course, horrible, and not humorous at all.

Stories tell of a boy in China who was impaled by an office chair. This chair was powered by a gas cylinder, and the cylinder exploded in 2009, blasting metal up his butt and killing him.

Could have been worse. Could have been a couple inches forward and not killed him.

We don’t want to spend too much time on that story, on the technicality that it’s likely completely made-up.

Almost certainly an urban legend, but you just checked your office chair, didn't you?

5. Bullion, Milk and Whiskey Up the Butt

I will admit to being somewhere in adulthood before I realized that bullion and bouillon were two different things. So I understand getting it wrong Both words come from the same root, a French word that translates to "boil," meaning like heating something to the point that liquid starts to turn into gas, not the painful pimply thing you get on your butt.

Had to relate it to butts somehow, in honor of the article.

Point being, they stuffed bouillon up the butt in question, not bullion, which would have made it harder to insert the milk and whiskey. Editing is dead. (The text in this section gets the spelling right.)

President James Garfield died in 1881, after an escaped lunatic shot him in the arm and back... He died, historians now say, not just from the bullets but from how the doctors treated him.

I'd heard this before, but purposely avoided all the details... until now.

They shoved liquified food up his butt — beef bouillon, eggs and milk, along with whiskey and opium. They couldn’t let him eat, they said, because the bullet might have perforated his intestines (it really hadn't).

See? They got "bouillon" right there, but made up for it by misspelling "liquefied." (In fairness, that might be an alternate spelling and not an incorrect one.)

As a final note on this, let's not take this to mean "don't trust medical science." I mean, sure, don't trust 19th-century medicine; we might have advanced somewhat in that area since 1881.

4. Bitten by Your Own Attack Dog

I can't do this one justice (pun intended, but you'll only get it if you read the actual link); you'll have to see the article.

3. Filled With Compressed Air

No, not the way you're thinking.

McCormack didn’t wind up with a hose nozzle up his anus through debatable means. McCormack fell on a hose, and the fitting ripped through the muscle of one buttock, which is an experience no one would desire.

I don't know about that; it's probably a whole subgenre of paraphilia.

This was a compressed air hose, connected to the brakes in his truck, and the air now flowed through the hose, entering the man.

Ow. Ow. Ow.

He felt like he were blowing up like a balloon. But he survived, and he’s now available for interviews about how the working class is dealing with inflation.

Oh, that's right: that one line is the actual reason I saved this article in my queue. I'm mad that I didn't think of it first.

2. Water Ski Douche

No.

But it only gets worse:

1. Cooked as Steaks and Fed to Children

Someone's been reading too much Brothers Grimm.

Knight went on to be the first woman in Australia to be sentenced to life without parole. Authorities have no firm advice on how to stop something like this from happening again.

I have some, hard-won from personal experience:

1) Don't go to continent/island/countries where it's well-known that everything, including scorned lovers, is out to kill you;

2) Don't stick it in crazy.

3 Like • Comment • View 1 comment

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