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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Write_Mikey_Write!

about 8 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 10 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.

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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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

January 13, 2024 at 10:56am

#1062329

Original Syndrome

This Atlas Obscura article (apparently from a writer at Big Think, which I've also sourced here) has been taunting me for a long time, waiting for its number to come up. Today, it finally did.

There Are at Least 10 Cities With Their Own Psychological Disorders
Stockholm Syndrome is the most famous, and most relate to tourism or hostage-taking.

I'd expect there to be a lot more than 10, but maybe there are. "At least" covers a lot of numerical territory.

Everybody knows Stockholm Syndrome, when hostages develop an attachment to their captors.

Like most things "everybody knows," there's doubt that this even exists

in the way they think it does.

But who knows its two opposites? Lima Syndrome is when the hostage takers start sympathizing with the hostages.

I mean, that makes sense. It's the inverse of Stockholm Syndrome, and it's kind of on the other side of the planet, hence the inversion.

And London Syndrome is when hostages become argumentative toward their captors—often with deadly results.

What are they going to do, kill us? Then they won't have hostages as leverage.

In all, ten cities around the world carry a unique burden: they have a psychological disorder named after them.

I don't need to rehash all of them here. Really, I just have one quibble (apart from questioning whether Stockholm Syndrome is really a thing):

Brooklyn Syndrome

...cities where, due to specific cultural circumstances, the male persona naturally gravitates toward being overly argumentative or personally combative.

It is simultaneously hilarious that they picked Brooklyn as the archetype for this kind of thing, and sad because Brooklyn isn't a city, but part of New York. Hey! I'm walkin' heah!

Instead, I wanted to propose other disorders named after cities. In no particular order.

Albuquerque Ailment: That nagging feeling that you shouldn't have taken that last turn.

Chicago Croup: A perverse desire to be someplace cold and windy.

Seattle Syndrome: The feeling that it really ought to be raining.

Montréal Malaise: Not knowing enough of the local language to carry on a conversation, but just enough to know when they're calling you names.

San Francisco Flu: Being too hot when the temperature climbs above 60F.

Washington Woozies: When someone drags you into an unwelcome political conversation.

...yeah, I know those are all in North America. It's not like I spend weeks refining my jokes. If you have suggestions for other cities, please feel free to add below.

7 Like • Comment • View 4 comments

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