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 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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2 Like

Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

July 18, 2024 at 12:31pm

#1074113

All In a Row

Got another "Journalistic Intentions"

[18+] entry today:

Jessica Fox

When it comes time to write on a subject about which I know next to nothing, my obvious first stop is Wikipedia.

Sure, it's not perfect, but is anything? Earning a gold medal in the Olympics is about as close as one can get.

And I do have respect for anyone talented and dedicated enough to do that. I also have respect for the talent and dedication required to be an opera singer, but that doesn't mean I want to subject myself to the experience of sitting through an opera.

As much as I enjoy learning new things, there's just not enough time to be interested in everything. Some things get pushed to the bottom of the queue, like opera or sports.

So while it may shock some people that today is the first time I've ever heard of Jessica Fox, today is the first time I've ever heard of Jessica Fox.

Would I have heard of this medal-collecting canoeist—that is, would some news story about her have impinged itself on my consciousness before now if she were from the US instead of Oz? Maybe. Maybe not. If so, that wouldn't be my fault. A lot of the news I get is from the US, but I also get information from international sources, and it's not like she's from some obscure country with a weird language. Okay, weird language, sure, but Australia is hardly obscure. In any case, I actively avoid sports reporting. It's a practice I inherited from my parents.

I'm sure it's somehow bad that my first thought was "sure, you pretty much have to be an Olympic athlete to outrun/outswim/outrow the local wildlife there." That's gone past the "tired old joke" phase to "always funny." It's especially funny because I'm pretty sure Australians promote the exaggeration in order to keep ugly Americans from wanting to visit.

It's not working on me. I'd love to visit, drop bears and all. The thing that's stopping me is the thought of a 24-hour-plus flight (with connections) cooped up in a flimsy aluminum can with a bunch of American tourists.

For shiggles, though, I just looked up some flights (I had to in order to confirm the duration), and the prices are remarkably reasonable. For riding steerage, anyway. Less than 2000 US dollars for a round trip with one stop. Yes, that's a lot of money, but not bad for flying nearly halfway around the Earth, which, I feel I must reiterate, is round.

But I digress. Remember up there I said I inherited an aversion to sports news from my parents? Apparently, things like that run in the family, because Fox's parents were also world-class paddlers.

I guess you could say they're all in the same boat.

4 Like • Comment • View 3 comments

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