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

March 13, 2023 at 1:28pm

#1046340

Begging, the Question

Let's tackle another prompt from "JAFBG"

[XGC]...

What's your opinion on people who are uninsured seeking donations after disasterous events?

Honestly don't give a shit.

Everyone knows, or should know, that insurance companies are wankers. Just the other day, I saw an article about how some of them lowballed payouts for their customers facing hurricane losses in the Wang of America. I apologize for the New York Post link,

but I saw the same story in WaPo (which is more respectable but paywalled).

It’s been more than four months since Hurricane Ian ransacked Florida’s Fort Myers Beach — but many residents are battling with insurance companies, and one family says they’ve been offered just $500 compensation for their house, which was left unlivable.

To be fair, lots of homes in the Wang are unlivable, hurricane or not. But generally not the ones in Fort Myers Beach.

In any case, the point is, insurance of any kind is kind of a gamble. Not like mad-money casino gambling, but even absent corporate shenanigans, you're paying for peace of mind. If nothing ever happens to your (whatever), then all that money was, in hindsight, wasted. But only in hindsight. Meanwhile, insurance companies have actuaries who, like the oddsmakers in a casino, determine, in aggregate, how much they have to charge in relation to expected payouts from claims in order for the CEO to buy a second (insured) yacht.

I'm not saying it's a scam, though it sometimes is. But the odds are not in your favor. It's largely about risk management, and while the odds are low that something bad will happen to your house (unless you live in Florida or near freight train lines), in the event that it does, the consequences, if you're not insured, can be doubly catastrophic.

Now, if you take the risk and don't get insurance, that's on you. Asking for donations? Well, it's not like you're, say, a bank demanding taxpayer bailout money; those donations are entirely voluntary. If someone feels sorry enough for you and has extra cash, so what? None of my damn business.

One would need to be mindful of the tax consequences, which I'm unclear on. Gifts are generally not taxable by the IRS in the US up to a certain amount; and, over that amount, oddly, as I understand it, the taxes are the responsibility of the donor, not the recipient. No, I don't understand it. No, it doesn't make sense. No, it doesn't have to make sense. But then (again based on my limited understanding), insurance payouts are also nontaxable. And I have less than no idea how other countries handle it.

I mean, I wouldn't give 'em a dime. But that's just me being an asshole.

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