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 9 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.

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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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

September 29, 2024 at 3:39am

#1077421

Bad to the Beaune

The association of Dijon with mustard is universally-known and inescapable, but I'm not here for the condiment; I'm here for the wine, because Dijon is also part of Burgundy. As I mentioned a few entries back, Burgundy (or Bourgogne) has a connection with wine that's also universally-known and inescapable.

Oddly enough, despite it lending its name to a particular shade of red (as detailed in an entry I did a while back, "Burgundy"

), the majority of the wines here are white; mostly Chardonnay. It makes a much better wine here than in the US.

In that entry, from way back in February, I said, "Incidentally, these blog entries are inadvertently helping me plan a trip to France." Et voilà, here I am.

But back to Beaune, which isn't actually pronounced like bone: it's south of Dijon and the road takes you through a multitude of vineyards and wine-producing villages. There, while others in my tour group grabbed snacks and ran through some historic sites, I dined at a very French restaurant. Well, I say "very French," but they have an English-language menu, so they do cater to tourists.

We only had two hours in Beaune, and, ideally, I'd have liked to seen the old stuff as well as enjoyed the food, but I couldn't do both. Faced with a choice, it will always be, in order: beer, wine, distilled spirits, food, history. And this place, naturally, offered wine with the food, which included the famous dish bœuf bourguignon. That dish is, of course, another famous cultural export of Burgundy.

The truly amazing thing, though, is this: the meal started with an apéritif, then an entrée with a glass of white Burgundy (recall that in French, entrée is like appetizer), then the bœuf bourguignon with a glass of red Burgundy, and, finally, a cheese plate. I was shocked that it only cost about 80 euros.

So, yeah, I wish I'd seen more of old Beaune, but I have my priorities. I hope to make up for it today by seeing some historical crap here in Dijon. And maybe pick up some mustard.

6 Like • Comment • View 1 comment

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