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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2 Like

Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

July 10, 2024 at 10:03am

#1073780

Phrase Turner

It's only been about a month, and I've already forgotten why I saved this articlebook ad from CNBC. But I'm sure I'll have some things to say, anyway.

Former CIA agent: 4 powerful, underutilized phrases can help you establish credibility and earn anyone's trust

In my career as a CIA analyst turned CEO and business advisor, understanding how to communicate effectively in complex and stressful environments has been at the core of everything I do.

That, and knowing how to spy on the competition without getting caught.

Ultimately, I've found that by leading with honesty and authenticity — and with some practice — anyone can learn how to meaningfully earn the trust of powerful stakeholders, and get them on your side.

Yep. People respond positively to honesty and authenticity. So once you've learned how to fake those things, you're golden.

Using these four key phrases have helped me become a better speaker and problem solver...

Oh, that's right. I thought this might be of interest to writers, as phrases are our stock-in-trade.

1. 'What information do you need?'

This has the added benefit of preventing you from giving away too much information, yourself.

I remember asking Senator John McCain this question during a foreign policy briefing once.

Nothing like name-dropping to show your street cred. "Yeah, I once had a casual conversation with a guy who at one point was just a few electoral votes away from becoming President."

2. 'Is there anyone else who needs to be part of this discussion?'

"Do you need to bring your mother here?"

3. 'Who disagrees?'

"And what dirt can we find on them to make them change their minds?"

4. 'I don't know, but I will find out and come back to you'

Okay, I can't really snark on this one. That's engineer-level thought right there. No one knows everything, and it's better to admit that you don't know than to make something up that might come back to bite you.

Just be sure to actually follow through.

Seriously, though, I don't think it's a bad articlead. And even I was impressed at the author's credentials at the bottom of the page. I just couldn't let certain jokes sit there, bored, with nothing to do.

6 Like • Comment • View 3 comments

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