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

December 30, 2020 at 12:01am

#1001035

Pigs on the Wing

"30-Day Blogging Challenge ON HIATUS" [13+]:
30. Bacon Day
The perfect breakfast meat.
Write anything about bacon!

Ah, yes, bacon... the candy of the meat world.

On the rare occasion that someone works up the chutzpah to ask me why I'm no longer a practicing Jew, I like to reply, "Tried bacon once, never looked back."

Which reminds me of an old joke:

A rabbi and a priest end up next to each other on an airplane. It's a long trip, so they get to talking. Eventually, they get comfortable enough with one another to ask the important theological questions.

"I'm curious," says the priest. "And you don't have to answer if it makes you uncomfortable, but... have you ever tried bacon?"

The rabbi sighs. "Yes, yes, I confess... in my younger, rebellious days, I once tried a bit of the forbidden meat. But it was only the once, never again."

They're silent for a while, then the rabbi goes, "I'm curious too, and you don't have to answer either, but... have you ever had sex?"

The priest goes, "Yes... yes, I have to confess that in my earlier, rebellious days, I did the act with a nice older lady. I did penance for it for weeks, and it was just the once, never again."

The rabbi sits back and nods. They're silent for a while again, and then the rabbi side-eyes the priest and mutters:

"Beats the hell out of bacon, doesn't it?"

Thank you, thank you, I'll be here all year.

But seriously, though, I, too, have a confession to make:

When it comes to breakfast meats, I prefer turkey "bacon."

Yes, yes, I know, I can hear your collective gasp of disbelief and astonishment all the way over here. But it's true. The thing about bacon -- about meat in general (and don't give me shit about not being vegetarian) -- is that I like the meat, but I do not like the taste of animal fat. And bacon is mostly fat. At least, American bacon is; what they call bacon in Britain is more like what we call Canadian bacon, which in Canada is called backbacon. It's leaner, anyway. And turkey "bacon," being made of bird, has far less fat to it.

Which doesn't mean I'll turn down actual bacon if it's around, of course. But it's gotta be completely cooked. If I hold it by one end, it should remain horizontal, with no measurable droop. And the despicable practice of cooking eggs in the bacon drippings? No.

Speaking of cooking bacon, there are only two acceptable methods: oven and microwave. In the oven, the strips need to be arranged on a rack with the drippings caught by a pan and then discarded. This is preferable to me, but can take up to 30 minutes, including preheating time, which is usually unacceptable in the morning. So for speed, I use the microwave method: three layers of paper towels, strips of bacon, then two more layers of paper towels. 2-3 minutes depending on the amount and thickness of the slices. The towels absorb the fat, leaving me with nice crispy bacon (one can cook it for less time for a chewier bacon, if you're one of those weirdos).

I've tried the vegetarian strips that are meant to pass for bacon. They do not, in fact, pass for bacon, even though the makers take great pains to make them look marbled. If you don't pretend they're bacon, though, they're not bad in themselves. I call it "fakon."

And great, now I'm hungry and oh look there is bacon in the fridge...

3 Like • Comment • View 6 comments

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