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:

Wordsmitty ✍️

about an hour 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?

1 Like

🌖 HuntersMoon

about 5 hours ago
In response to "Gray Matters"

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

1 Like

tj-Merry Mischief Maker

about 24 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

June 2, 2024 at 10:06am

#1072011

Revisited: "Nonbinary"

As regulars know, I do these retrospectives, in part, to see what's changed about the world and in me since the original post. Usually, I don't find my attitude much different. That's not really the case with this entry from February of 2020: "Nonbinary"

Today's thing is a bit different from usual: a gender-issues retrospective from a male homo sapiens.

For starters, I cringe at "different from."

The article

in question, from 2018, is still up at this time, but I didn't re-read most of it.

Not only is the weight issue a pressing thing for many men, but I avoid online dating specifically because most of the women on there specify 6' or taller.

That's actually not the only reason I avoid online dating. But I wonder what some of these women's reaction would be to a man who requires "natural D-cup or larger only." Not great, I'd imagine.

I can do something about my weight, and I am.

Turned out I couldn't, so I stopped trying.

Can't do anything about my height.

Since then, I've seen pieces about some kind of surgery that puts extenders in your leg bones to make you taller. The surgery isn't risk-free, and from all accounts, it's painful with a fairly long recovery time. Not worth it, in my book.

We desperately need "accept yourself as you are" messages, but there's no money in that, so instead we're stuck with "you're just not good enough, but if you buy my crap, you'll finally be satisfied." (Spoiler alert: you'll never be satisfied.)

What's height got to do with anything besides blocking the people behind you in the theater?

I recently read an article in which some vapid lady expressed a desire to be "swept off her feet" both literally and physically, and apparently that could only be done by a 6'+ man? Okay, well, I wouldn't be interested in her, either.

I have to admit, as an aside, that I find it hard to see the whole "gender is a social construct" thing. I mean, yes, certain aspects of it are, in my view, but they're mostly superficial things: a particular style of haircut, wearing bigger watches (if one wears a watch at all these days), a lack of makeup.

Since then, I've come around more to to that point of view.

Basically, if something is a social construct, the social construct can be changed.

I stand by the "can be," but I recognize that those things take time, often longer than a human lifespan.

One of the greatest failings of modern society, I think, is this "binary" myth.

Standing by this statement, too. I've railed on binary thinking many times since then. And no, this isn't limited to the male/female binary; I think Netflix jumped the shark, for example, when it removed star ratings in favor of Siskel and Ebert style thumbs. But, lest anyone be confused by the entry's title, this sort of thing is what it referred to.

But still, my views have evolved somewhat. One thing, though, that I hope never changes about me:

And everyone deserves basic human dignity and rights (at least until they prove themselves unworthy of such by their actions), regardless of what pigeonhole you or society says they belong in.

I trust that's clear enough.

3 Like • Comment • View 1 comment

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