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.

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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.

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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.

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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

February 9, 2021 at 12:01am

#1004024

Vile, Virile Vices

I always find it amusing, in a dark-humor sort of way, how often groups of people flee religious persecution so that they can install their own.

America’s First Banned Book Really Ticked Off the Plymouth Puritans

Few examples are more obvious than the Puritan settlers of Massachusetts. And while the land they settled eventually came around to the ideals of freedom of religion and expression -- well, at least up to a certain point -- their insistence on a narrow view of morality echoes to this day like the reverberating sound of a turd hitting the slurry at the bottom of an outhouse.

Apparently, Thomas Morton didn’t get the memo. The English businessman arrived in Massachusetts in 1624 with the Puritans, but he wasn’t exactly on board with the strict, insular, and pious society they had hoped to build for themselves.

Why would such a person brave an uncertain ocean journey with such horrible people? Why, money, of course.

The Puritans’ move across the pond was motivated by both religion and commerce, but Morton was there only for the latter reason, as one of the owners of the Wollaston Company.

Who?

His business partner—slave-owning Richard Wollaston—moved south to Virginia to expand the company’s business...

I'd suggest cancelling this guy, but it seems history already has.

...but Morton was already deeply attached to the land, in a way his more religious neighbors likely couldn’t understand. “He was extremely responsive to the natural world and had very friendly relations with the Indians,” says Heath, while “the Puritans took the opposite stance: that the natural world was a howling wilderness, and the Indians were wild men that needed to be suppressed.”

It's funny because the researcher's name is Heath, which is a word for an area in a state of nature, which gave us the word "heathen."

After Wollaston left, Morton enlisted the help of some brave recruits—both English and Native—to establish the breakoff settlement of Ma-Re Mount, also known as Merrymount, preserved today in the Quincy neighborhood and park of the same name.

Incidentally, if you're not aware, Quincy is pronounced like "quin'-zee." Just in case you find yourself in the Boston area one day, don't get tripped up by this shibboleth.

The Puritan authorities didn’t see Merrymount as a free-wheeling annoyance; they saw an existential threat.

Of course they did. The thing most frightening to a Puritan is the horrible idea that someone, somewhere, is having a good time.

With Plymouth’s monopoly dissolved and its perceived enemies armed, Morton had perhaps done more than anyone else to undermine the Puritan project in Massachusetts.

I should absolutely build a shrine to this guy.

Worse yet, in the words of Plymouth’s governor William Bradford, Morton condoned “dancing and frisking together” with the Native Americans—activities that were banned even without Native American participation.

Snort. "Frisking." Snort. Which reminds me of a joke. Why aren't Puritan kids allowed to make out? Because it might lead to dancing.

There could be no greater symbol of such misrule than Morton’s maypole. Reaching 80 feet into the air, the structure conjured all the vile, virile vices of Merry England that the Puritans had hoped to leave behind.

I'm absolutely, totally stealing "vile, virile vices." Oh, wait, I already did, for this entry's title.

The article goes on to talk about the book in the title of the piece, and I feel like I really should own a facsimile of it (I'm not quite impressed, or rich, enough to try to track down a first edition).

After publishing the book, Morton braved a venture back to his beloved Massachusetts, only to be turned right back around upon arrival. He tried to cross the Atlantic once again in 1643, and was this time exiled to Maine, where he died.

There are probably worse fates, but I can't think of any offhand.

So, a short read, and worth it -- and the source, Atlas Obscura is a wonderful fount of information. The only problem is they keep posting places to visit in Belgium, and I don't know if I'll be able to go to them all.

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