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').

1 Like

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

1 Like

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

December 15, 2020 at 12:02am

#1000256

I Never Herd Of Such A Thing

"30-Day Blogging Challenge ON HIATUS" [13+]:
15. Cat Herder's Day
Ya, good luck with that.

"JAFBG" [XGC]:
Tell us about something/someone that fucked you off this week.

Women and cats will do as they please, and men and dogs should relax and get used to the idea.
-Robert A. Heinlein

Yes, Heinlein was a bit of a sexist. He grew up in an entirely different time.

Still, that's a quote that I took to heart -- not for the sexist overtones; I figured the truth is "people and cats will do as they please," and I try not to concern myself with making other people do things. Nor do I worry about herding cats. Feed the cats, pet them, play with them, make sure they're healthy, and they'll stick around and do very cute and silly things. If I wanted to exert control over something -- which I don't -- I'd get a dog. Which I won't.

It's really about accepting those things you can't change.

And you know what else I can't change?

SEGUÉ

Insurance company bullshit.

Okay, this wasn't this week but last week and it's only Monday so it counts.

Some background: Last year, I didn't have health insurance. It would have been entirely too expensive. At the end of the year, though, I looked into new options on the ACA website, and found a plan I could live with. It's still very expensive, and has a high deductible, but I have it in case something major happens, at which point I fully expect the insurance company to fight my claim tooth and nail. But then again, they might not, so if I go to the ER for a hangnail and they charge me $150,000 for a band-aid and some Neosporin, hopefully the insurance will cover most of that.

But what sucks about the insurance is the prescription foolery.

Like many people, I've been prescribed a statin for cholesterol control. The doctor gives me a 90-day prescription with refills enough to last almost a full year (90x4 = 360, which is 5 days less than most years). I go to the pharmacy to get it filled, and suddenly it's a 30-day prescription and I'm charged about $30 for it. Okay, that's not terrible; obviously it works out to a dollar a day. Fine. But now I have to walk into a pharmacy during a pandemic every month instead of every three months.

So I look into it further. It turns out that if I pretend I don't have insurance and just buy the 90-day prescription outright, it costs -- get this, now -- $33.

That's right. A 90-day supply of this crap without insurance costs 1/3 as much as three 30-day fills with insurance.

The only downside is that the price of the prescription doesn't apply to my yearly deductible, but look, if I ever have occasion to exceed the deductible, that extra ($30x12=) $360 isn't going to change shit.

Right now every American reading this is nodding knowingly, while every non-American is confused as shit. Don't worry. It confuses us too.

But what can you do? Arguing with insurance companies is like trying to herd cats.

8 Like • Comment • View 6 comments

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