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 6 hours 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.

1 Like

🐕GeminiGem🎁

about 10 hours ago
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

about 12 hours ago
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

about 12 hours ago
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

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

November 12, 2024 at 8:41am

#1079840

Blond Man's Bluff

Sometimes, I link to Cracked for its take on serious topics. Sometimes, though, it's because of jokes.

The Funniest Blonde Jokes Ever Told

Historical blonde jokes aren’t as well-documented as other classics, like fart jokes, for example.

Fart jokes may be "classic" (the oldest recorded joke is one of them), but they are the lowest form of humor, unlike highbrow amusements such as dead-baby jokes.

The people who study this type of thing tend to agree that they’re just lazily recycled versions of older jokes, that replace racism and xenophobia with sexism.

Yeah, not exactly a step up.

But the genre does have some notable subversions!

The thing about subversion is you need to be familiar with the thing that's being subverted, and hardly anyone tells blonde jokes anymore, so some people might not get the twists.

5 ‘The First Officially Recorded Dumb Blonde’

This is included for historical context.

Catherine-Rosalie Gerard Duthé was a French nun, ballet dancer and courtesan in the late 18th and early 19th centuries.

We should be concentrating on French jokes, not dumb blonde jokes.

She had a particularly notable habit of “pausing for extended periods of time before speaking.” Some might call this act “thinking,” but the French decided this made her dumber than a beret full of baguettes.

One wonders whether this contributed directly to the French Revolution.

4 Meta Blonde Jokes

You know how a blonde joke works. A brunette, a redhead and a blonde do something, the blonde does it wrong, because she’s dumb and incapable, the patriarchy grows stronger.

Worth going to the link just for the joke here.

3 The Counter-Revolution

A notable, though flawed, early ally was cartoonist Murat Bernard Young, who drew two extremely popular comic strips. Dumb Dora was about a space cadet brunette, while Blondie was about a smart, capable mother whose husband was the bumbling, glassy-eyed doofus.

The "bumbling, glassy-eyed doofus" trope continues to this day (Homer Simpson, e.g.), but apparently, it's okay to make men look stupid.

2 Existentialist Blonde Jokes

The New Yorker’s “Existentialist Blonde Jokes,” written by Alex Baia back in 2021, subverts some of the most tired blonde jokes out there...

I rag on The New Yorker on a regular basis, because it's pretentious as fuck, but one thing it's usually gotten right is comedy. I'll just copy one of the jokes here:

How do you drown a blonde?

Remind her that life is inane, repetitive and intrinsically meaningless.

1 Blonde Jokes for Men

Ever wonder about the difference between blonde and blond? It's not like gray/grey, which is largely a difference in US and UK/Commonwealth English. It's because "blond(e)" is French, so it possesses grammatical gender. Women are blonde; men are blond. It's one of those few words we stole from French that kept its inflections, like fiancé/fiancée.

Anyway, like I said, there's no need to specify the man's hair color. Many of us don't have any, anyway, and we're all stupid and bumbling, regardless of coiffure.

1 Like • Comment • View 1 comment

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