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 20 hours 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

a day ago
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?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

August 2, 2024 at 11:14am

#1074681

Don't Bank On It

Today in You're Doing It Wrong: Banking.

Why You Need a Backup Bank
Your bank can close your accounts, refuse to deposit checks, or do anything else at any time. You need a Plan B.

Well, if that's the case, why use a bank at all? Oh, yeah, because if you keep cash around, eventually the cops will find out and seize it all through civil forfeiture.

I know some people will be like "Bank? I don't hang on to money long enough to need a bank!" This article, then, is not aimed at you.

Banks can refuse to let you open an account in the first place, refuse to accept a check for deposit at their discretion, and can close out your accounts and send you—and your money—packing any time they want, for a wide variety of reasons.

I suppose that's still better than sending you packing while keeping the money.

It’s a nightmarish scenario: You have a checking account with Bank A, where your paychecks are directly deposited and from which you pay all of your bills. One morning you wake up to a long list of bounced checks, failed debits, and late fees—and a note from Bank A that your account has been closed due to “suspicious activity,” or some other vague reason.

One wonders just how probable this is. I've heard of it happening, but it's never happened to me or anyone around me that I know of. The article says it happens "all the time," but as you've probably figured out, there are other examples of hyperbole in the text. One of the links there directs to a news story that mentions, specifically, Bank of America.

Thing is, if you're still banking with one of those huge national banks... why? The purpose of their existence is to screw you.

A backup bank account can also act as quasi-emergency fund. A checking account at Bank B likely won’t be earning much interest, but it will also likely sit undisturbed, and since it’s not directly connected to your daily spending, you won’t be regularly tempted to dip into it.

Also, I can't help but feel like the article is making a lot of assumptions: that you have a job, that you have spare money, etc. I think that to many people, the idea of having enough cash to bother with one bank, let alone two, is laughable. I suppose one can make the argument that to read the article, you have to be in a position to at least have internet access, which implies you're in a place where that's possible. Still, when I was poor, it might as well have been "How to Save Money on Yacht Maintenance."

Don't get me wrong; I'm a big fan of having backup plans. It's like carrying a spare tire in your car. But that assumes you're in a position to own a car in the first place.

5 Like • Comment • View 2 comments

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