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 23, 2024 at 9:14am

#1074310

Holy of Holies

This month's penultimate entry for "Journalistic Intentions"

[18+] takes us to the Great White North.

Montreal

A while back, a friend of mine was getting ready to visit NYC for the first time. (I promise this is relevant to the prompt.) She knows I go there fairly regularly, but every time I wanted to give her advice or suggestions, I managed to restrain myself. "I'll answer questions if she asks," I thought to myself. "It's more fun to discover things for yourself there."

And then, one day, she texted me with, "Where's the best place to get bagels?"

I immediately responded with "Montréal."

"Asshole."

There are, of course, plenty of great bagel places in New York. While I can't personally vouch for the "Montréal" answer, having never been there, I've heard it from so many different sources that I have accepted this superlative as Truth.

Which led me to wonder: How did this Francophone city in the upper reaches of North America become the Holy of Holies? (Get it, because bagels have holes? I'll be here all week.)

Obviously, it has to do with the Jewish community there. But the origins of this particular toroidal carbohydrate module stretch back, not to France, but to Poland. Like every near-perfect food, such as curry or pizza, though, they proved too popular to be limited to one country, instead spreading in their glorious roundness all over the globe.

It's true, however, that bagels entered the North American diet by way of New York, not Montréal. But they spread like cream cheese on a... well, they spread. Hell, there's even a great and popular bagel place right here in my very Southern hometown.

It's even one of the few foods that California does right. They can't make a decent pizza or pastrami sandwich, but there are at least good bagels scattered around California like poppy seeds on a... well, they're scattered.

As a side note, I once had a pastrami pizza. I was, of course, initially skeptical, but that particular abomination turned out to be quite delicious. Where was it? South freakin' Dakota, and I never would have discovered it had I not been stranded there for two days.

But I digress. We were talking about... what were we talking about? Montréal. I thought about going there before France, mostly to try the bagels. But I was concerned that I'd miss summer. There's a three-day window when the climate there would actually be comfortable for me; the problem is, one never knows exactly when those three days fall on the calendar. Usually in July, but not always.

Bagels, however, are a multi-season food. You know, many seasons. Like on an everything bagel.

4 Like • Comment

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