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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Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 14 hours ago
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

about 18 hours ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

about 21 hours ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

a day 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

Dec 24, 2024 at 5:16pm
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

May 5, 2024 at 7:04am

#1070539

Revisited: "Fail"

We're going back in time, as usual for Sunday mornings. This time, it's just to October of 2020 (specifically, 10/10/20, one of the few dates that work in both American and European style conventions and which can also be turned into a mathematical equation): "Fail"

I did the entry for that month's round of "Journalistic Intentions"

[18+], which is still an active blogging challenge, though not every month. Also, all the links in the entry are still solid, which isn't too surprising for something less than 4 years old.

Anyway, I got curious and looked up the origin of the name Fail.

I didn't go into this at the time, but today, I noticed that the ultimate origin of the Scottish surname Fail (which has many alternative spellings) is the name Paul. Don't ask me what kind of linguistic vowel shifts it takes to get from Paul to Fail; I don't know. But the name Paul, from Paulus, is Latin in origin, though it is probably most associated with the Paul of the New Testament.

So Paul becomes Phaill (or some similar spelling), and, by the convention of some Scottish clan names, generates MacPhaill, later Anglicized as MacFail or just Fail.

At least, that's one possible explanation. I never did trust some of these genealogy websites. But you know the Meat Loaf character in Fight Club? "His name was Robert Paulson." Well, "Paulson" is the English equivalent of MacPaul, which we've already speculated became the name Fail, so I have to wonder if Palahniuk did that shit on purpose. Probably not; his symbolism tends to be more of a, well, a punch in the face.

Anyway, back to my original entry:

I know, I know, it's rude to make fun of peoples' last names. You should be proud of your last name, even if it's Fail.

Or Hogg, as in yesterday's entry (coincidentally, also Scottish). Still, being proud of being a Hogg (or a Fail, for that matter) is no damn excuse to name your kid Ima.

There's the story of a Dr. A. Hedgeh, for example, who apparently had a problem with people adding "og" to his nameplate.

In case you don't want to bother rereading my 2020 entry, I'm including that link

here again, because I still laugh every time I see it. Fake or not.

So, yes, it's rude to make fun of peoples' names.

But sometimes, it's so funny you can't help it.

3 Like • Comment • View 1 comment

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