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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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 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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