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 31, 2023 at 10:45am

#1047230

Being a Pill

Very close to completing all the prompts at "JAFBG"

[XGC]...

Tell us about something/someone that fucked you off this week.

Ah, yes, the recurring reason to rant. Thing is, if I'd drawn this prompt with my random numbers earlier this month, I would have been stumped. For most of it, I didn't experience more than minor inconvenience, nothing worthy of a full-blown rant.

All that changed starting last Saturday.

Friday, with two pills left in each of my daily prescriptions, I called the pharmacy for refills. This is an automated system, which is fine; you just key in the prescription number for each one, the robot confirms it, and then, when you're done, you get told when they'll be ready for pickup. In this case, they clearly and unambiguously said "Saturday at 11 am."

Now, there's something else you need to know about my prescriptions. I think I've ranted about it before, but just to recap: My insurance sucks. The doctor sends a prescription for a 90-day supply. If I use my insurance, I have to get a 30-day supply, and it costs about $30. Here's the whatthe part: If I don't use insurance for the prescription, they happily sell me a 90-day supply. For about $30.

You read that right: With insurance, $90 for a 90-day supply. Without insurance, $30 for a 90-day supply.

There are other details, but that's the outline of it. So, getting back to the timeline here, remember, the prescriptions would be ready by 11am on Saturday. Well, I had other stuff to do Saturday, so I showed up at the pharmacy at 3pm. This particular pharmacy is in a grocery store, and I'm pretty sure they have standing orders to delay things to encourage people to shop. Still, I fully expected that, having been told the pills would be ready at 11, surely, definitely, without fail, they'd be done four hours later?

If you're reading this, you can guess what didn't happen.

And this wasn't the usual "oh, it'll be ready in 20 minutes; why don't you take a look at our lovely endcap displays and seasonal merchandise while you wait." No, it was "It might take an hour or so, if you want to come back." Well, I told them I'd come back the next day. Which was, if you've been keeping track, Sunday.

I walk in and the cashier is like "I can't find it."

I felt rage boiling up inside me. None of those pills are specifically for rage, either pro or con, but I'd cut it too close: failure to receive my prescriptions that day would mean missing at least one dose. Which, to be fair, probably wouldn't kill me, but I'd feel obligated to report it to my doctor later, and she'd undoubtedly shake her head in disapproval. Which is crushing.

So it wasn't really about the pills themselves, at this point. It was more about being jerked around by robots and cashiers. "But Waltz, isn't that just another minor inconvenience?" Yes, except that I have to deal with some kind of bullshit every time I get the pills, which, if you're following along, you know is four times a year. It wears on me. At least it's not 12 times a year, though, right?

My boil was short-lived, however; she somehow found the prescriptions. But then my brain went to: "Okay, if they forgot and used insurance, I'm going to blow my shit."

Fortunately, everything was in order. So the saga ends, anticlimactically, but at least without bloodshed.

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