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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 2 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 4 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

January 12, 2023 at 12:02am

#1043012

Librarians

Getting back to articles, here's one from Cracked that should be of interest to readers. Since you're reading this, I assume you're a reader.

5 Ways Libraries Used to Be Hardcore

The title should more properly be "Ways Librarians Used to Be Hardcore."

While every profession employs miserable people doing jobs just because they’re told to, librarians are an exception. Librarians are heroes.

Every hero needs a catchphrase. For librarians, traditionally, it's "Shh."

5. Libraries Sterilized or Even Incinerated Books, and Laws Kept the Sick From Borrowing

We used to care about public health.

You were touching all these items that other people had fondled, people whose hygiene and morals you had no way to evaluate. We don’t have many public shoe exchanges, or rent-a-bra companies, because despite the obvious advantages of such facilities, such ideas repulse people. Maybe we should be just as weirded out by borrowing books.

Unlike with machines in gyms, there's no "wipe the books down when you're done."

Fuel for these fears came from a scientist named William R. Reinick, writing in the American Journal of Pharmacy. Someone once caught smallpox from a book, he said. Someone caught gonorrhea from a book, he claimed (exactly what they’d been doing to the book, he did not say). You could even catch cancer from books, he asserted. Then he shared the results of an experiment, where he kept 40 guinea pigs and gave them library book paper as bedding. All the guinea pigs died. This was damning evidence, if you don’t know much about how experiments are supposed to have control groups.

And also that guinea pigs live about two years, anyway, if they're lucky. Not to mention those suckers will eat anything, and I'd think it more likely the ink poisoned them.

Then as now, such studies were usually publicized so that the studier could sell their solution to the problem they've just created.

Some health measures make sense, while others do not. Examining books tells us that, yeah, they might have some germs on them, but still, it seems no one ever gets sick from handling books.

4. During the Depression, Librarians Went Out on Horseback to Bring Books to Mountain Folk

These mounted quests weren’t easy. Sometimes, the horse (or mule) would keel over and die. The librarian would have to continue the remaining many miles on foot. Sometimes, locals didn’t take kindly to these strange women bearing written words, forced on them by the government.

Nice to know nothing's changed in 90 years, except the caliber of firearms used to shoot at trespassers.

3. Librarians Put on Uniforms and Went to War (as Librarians)

"Bang!" "Shh!"

In Vilnius, Lithuania, the Nazis set up a Jewish ghetto and banned anyone from entering or leaving. Librarian Ona Šimaitė managed to go in and out anyway, using the excuse that she was collecting overdue library books. During these trips, she smuggled in food and arms, and smuggled out documents for preservation. She also smuggled out children, in sacks.

Legitimate badassery, right there.

2. Police Arrested People in the Middle of the Night Out of Their Beds for Overdue Books

Take New Jersey in 1961. Harold Roth, the director of the East Orange Public Library, decided he was through waiting on people to return their late books, and so, he called in the police. The cops staged midnight raids on 14 homes. People who had cash on them to pay the fines did so, while others had to go right to jail.

Fortunately, jails have libraries.

Today, libraries find that abolishing fines is actually the more effective tactic at getting tardy patrons to bring their books back.

"What are you in for?"

"Murder, rape, larceny, rape, resisting arrest, rape, and loitering. You?"

"Overdue library book."

1. J.P. Morgan Locked the Nation’s Financiers in a Library Till They Agreed to Bail the Country Out

This one was interesting to me because it involves a place I've actually visited.

In 1907, the economy was in real trouble. ...the burden for saving the country fell on J.P. Morgan. J.P. Morgan, librarian.

It's a stretch to relate this to librarianism, though technically it happened in a library, albeit a private one at the time. It's still a really interesting bit of history. Full disclosure, though, I couldn't be arsed to fact-check it, and I don't recall seeing any plaques about it when I visited the building in question.

Hell, I don't think most people have heard of the financial crisis of 1907, though it's what led to the formation of the Federal Reserve System. It was comparatively brief, and later overshadowed by the Great Depression (see #4 above).

The country survived, as did the library. Visit it today, to see some books, or to see a third-century Roman sarcophagus that Morgan installed.

The building in question, since the article neglects to mention this, is on Madison Avenue, a short walk from the Empire State Building. I don't remember the sarcophagus, though.

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