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 8 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🎁

a day 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

a day ago
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

a day 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.

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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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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.

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September 22, 2024 at 2:16am

#1077115

Landmarks

I don't use fitness apps, so I have no idea how many steps I took yesterday, or how many kilometers they added up to. But both numbers were very, very high.

While I was still exhausted from the trip, my contact here texted me around lunchtime. We'd never met. A mutual friend introduced us. It's probably only the mutual friend that kept us from going "what if the other's a psycho killer?"

Anyway, she's like "I'll be at [landmark] and we can meet at 1 o'clock." (She's American, incidentally, so we're texting in English.) At that point, it was 12:10. I checked Maps. Walking to [landmark] would take 45 minutes. I can just make it...

...except that I'd be walking through one of the most historic and architecturally interesting parts of Paris, and there is no way I would be able to resist stopping and gawking at something. Especially when the destination was on the other side of the Seine, and what foreign tourist can NOT stop and look at the river while crossing it? Maybe someone with more self-control than I have, but certainly not me.

So we met here at the hotel and started walking. I won't bother you with all the world-famous shit I saw yesterday, but there was a lot of it and it's world-famous and it's still thrilling to see that shit in person. Just one example: my hotel is a couple of blocks from the Louvre. Well, a couple of blocks from one corner of it, maybe a kilometer from the opposite corner. It's that big. Even without going in, the building itself is a work of art. And we didn't go in anywhere; it was Saturday and the tourism was in full force, creating chaotic crowds.

Hours later, we parted, and I made my utterly exhausted way back to the hotel. Along the way, though, I paused to snap a picture of perhaps the most culturally significant of all of Paris' landmarks, located on Rue de Rivoli.

Because, though I may have gotten some of the details wrong, it was here where, sometime around 1990, famed American visitor Vincent Barbarino discovered that, in France, a Quarter Pounder with Cheese is not, in fact, called a Quarter Pounder with Cheese, but a Royale with Cheese. Because of the metric system. These events were related in the documentary, "Pulp Fiction," which depicted quite the embarrassing and tragic ending for Vincent, but at least he got to spend time in fine Parisian restaurants.

6 Like • Comment • View 2 comments

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