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 7, 2024 at 10:07am

#1073635

Revisited: "The End is Nigh"

I was far more prone to writing really short blog entries in the far-distant past, like this one from December of 2007: "The End is Nigh"

Partly, it's because the Newsfeed hadn't been invented yet. I don't remember exactly when WDC added that feature. It was a while ago, but certainly not as far back as 2007.

But also, I think I had it in my head to write something every day, even if it was brief. Thus, you get utterly useless posts like that one. Nowadays, I still try to write something every day (at which I've been successful for about four and a half years, now), but I do try to make it worthwhile. Usually.

The end of the year, that is.

That, of course, referred to the clickbait title of the entry.

It doesn't feel like the end of the year. In fact, it feels like 2007 has just gotten started. That may be because I'm still working toward the same goals, trying to get the same stuff done.

Oh, to be young again and have "goals" and stuff to "get done."

Okay, traveling may count as a goal; I don't know.

Whatever.

Ah, yes, the rallying cry of my generation!

Tuesday is just another day (except, of course, for certain writing.com activities).

December 29, the date of that entry, was on a Saturday; by "Tuesday," apparently, I was referring to the day of January 1, 2008.

I have no idea what activities Past Me was talking about.

And just like always, first I have to make it through Sunday

Nor do I have the foggiest clue what he was going on about with that. Sundays have never been particularly onerous for me, insofar as I can recall. At the time, I was actively running a business, which meant that sometimes I had to work on Sundays (and Saturdays, and holidays, and evenings), but rarely was that the case during those liminal days leading up to the new year.

Also cringeworthy: I ended the entry with a smiley-face emoticon.

5 Like • Comment • View 1 comment

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