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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Writer_Mike

about 13 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

Sep 21, 2024 at 7:34am
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:46am
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

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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