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 11 hours 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

a day 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

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

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?

July 13, 2024 at 10:34am

#1073898

Surprise Me

A brief travel planning update:

I met with the travel agent on Wednesday. As a reminder, I'm using a travel agent this time because a) I'm entirely too lazy to coordinate my own itinerary; b) I don't know exactly what I want; and c) I've never done it before, so it'll be a new experience for me.

I told her basically what I wanted to do (wine and beer tourism in France and Belgium), so she suggested three locations in France: Loire, Burgundy, and Paris.

"So you'll fly into Paris and spend... how long there? Five days?" (I'd told her maybe three weeks for the entire trip.)

I'm like, "I'm not exceptionally interested in Paris. The city is dirty, and the people are rude and will be tired of foreign tourists after the Olympics."

I mean, I get flying into Paris. There's a big international airport there, and the other places I want to visit are generally in the northern part of the country. But thinking I want to spend time there is a big assumption.

Then I remembered that I'd heard the Paris craft beer scene had developed nicely in the past few years. Plus, she dangled "reservations at a Michelin-starred restaurant" in my hungry face. (I think they make most of their money from kickbacks, which is fine.) So okay, sure, Paris. Just not a lot of the touristy places. And maybe three days, not five. I know it's an enormous city and you can spend years there without running out of new things to do, but I'd rather focus on other locations.

The rest of the trip is countryside and small towns. Well, mostly. Nothing's detailed yet, but Belgium might involve staying in Brussels, for which I don't have any objection.

The problem with France, I've found, is that there's pretty much nowhere in the entire country that I don't want to spend time in. Well, maybe some of the freezing cold snow-peaked mountain parts. I wouldn't mind visiting them briefly, or seeing them from a warm, comfortable distance, but, as with every other high mountain range, the combination of colder temperatures and lack of air pressure is anathema to me. Plus, I might be expected to "ski," or "hike," or do any number of disgusting outdoor activities.

Yes, I've done it, like when I spent a week at a science camp in the Colorado Rockies. That's how I know it's not for me.

So, now I'm waiting for them to stitch together a draft of a travel plan. I'll get to look at it and change things if I want. I told her, "Don't worry; I like surprises... but only if they're pleasant ones."

She didn't find that nearly as amusing as I did.

5 Like • Comment • View 3 comments

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