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.

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September 25, 2024 at 1:42pm

#1077271

There Is A Such Thing As Coincidence

Yesterday's adventure took me on the TGV from Paris to Tours.

Don't ask me what the letters stand for. You can look it up same as I could, but I don't really want to know. Far as I'm concerned, they stand for Train Go Vwhooosh!

Out of curiosity, while on the train, I checked a website that used GPS data to determine one's current speed. Now, obviously, French high-speed rail can only move in km/h, and I can convert just fine in my head, but having spent most of my life moving at mph, I clocked in at 180-190mph.

Upon arrival in Tours, I made the questionable decision to walk to my hotel. Google said it was mostly flat, and it didn't lie. What it didn't tell me was that it was also mostly tiled sidewalks. Try rolling two suitcases on tiled sidewalks for 1600 meters.

The travel agent had some suggestions for what to do in Tours for the rest of the afternoon, and they were good suggestions, involving historic neighborhoods and buildings. I like that sort of thing well enough, but I have my priorities, so I set out to find beer.

What I found was very good beer, and a couple of hours later, I staggered back to the hotel, only to find, upon logging in to WDC, that our very own Annette

was, by cosmic coincidence, also in Tours at that moment.

So of course I had to stagger all the way to where she was staying which was, comically, right next to the train station.

At least I wasn't dragging luggage, this time.

Now, look, I don't just go knocking on random peoples' doors, even if they are regulars here on Writing.com. But I'd spent a week in the L.A. area a while back, being shepherded around by Annette and her husband. So it's not like we didn't know each other. I didn't knock on her door, either; we met in the lobby and went to have drinks. Soft drinks, because even I have my limits.

I got back to the hotel just after midnight, which probably wasn't the best idea, either; I had to get up at some ungodly cow-milking hour this morning to go on a planned-and-paid-for tour of some of the catwaters in the area. Catwaters? Wait, no, I mean chateaux. (The best part about learning another language is gaining the ability to make horrible puns in both languages.) But that's a discussion for tomorrow.

Pic posted with permission:

8 Like • Comment • View 4 comments

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