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:

Wordsmitty ✍️

about 2 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?

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

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

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 25, 2024 at 7:57am

#1073156

Can't Spell Success without Sucs

Okay. Fine. Sometimes, clickbait works on me. It draws me in, fuels my outrage, makes me want to read more so I can rant about it..

Richard Branson says money isn't a good way to measure success: Focus on this 1 word instead, it's 'all that really matters'

Which is exactly the kind of thing I would say if I were a billionaire and the poors kept grumbling about dragging me and my head to a guillotine. It's like when they try to convince us that "money can't buy happiness" while they're flying in their private jets, smiling and sipping a gin and tonic made with low-paid laborer tears.

But let's hear this rich guy's take on it, anyway.

Richard Branson doesn't want to be defined by his money.

Well, you could give it all away and see how you're defined then. (Preferably, to me.)

"Maybe in America, 'billionaire' is a sign of success, but that rankles me," says Branson. "I think that your reputation is what you create."

Didn't his company declare bankruptcy recently? Oh, yeah, one of them did, last year.

Such success.

The company is largely responsible for his estimated net worth of $2.5 billion, according to Forbes — but he chafes at the idea he created it to make money.

Bet he wouldn't have done it if he didn't think it'd be profitable, though.

In fairness, $2.5 billion is small potatoes compared to people like Bezos or Musk, both of whom I mention because they're his direct competitors in the spaceflight field.

Of course, success is never guaranteed. If you do follow your passions, you'll still need factors like talent and perseverance on your side to avoid falling flat, experts say.

Mostly, though, you need luck.

And the real reason I decided to snark on this article? (In truth, I have nothing against Branson.) It's that the article ends with a promotion for one of its publisher's offerings, and the ad begins with the bolded phrase: Want to make extra money outside of your day job?

Still not sure if that constitutes irony or not, but I got a good laugh out of it.

Regardless, sure, success can only be defined by the individual. But having lots of money, no matter what problems it might bring with it, is always better than wondering how you're going to make rent next month.

7 Like • Comment • View 2 comments

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