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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Annette in France

about 9 hours ago
In response to "It's Hot in The South, Once Again!"

The quote is too small and low contrast to be read.

Elycia Lee ☮

about 19 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

a day ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

a day ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

Sep 25, 2024 at 7:53pm
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

Sep 25, 2024 at 3:20pm
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

Sep 25, 2024 at 2:49pm
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

August 18, 2019 at 1:55am

#964364

The Inevitable

Yes, I'm in Vegas. Yes, I'm done indulging my vices for the day. Consequently... blog post. Warning: I've been drinking, so I may say shit I shouldn't.

https://www.vice.com/en_us/article/vbwpdb/the-climate-change-paper-so-depressing...

The Climate Change Paper So Depressing It's Sending People to Therapy
On average, three people read an academic paper. At least 100,000 have read this—and a lot of them haven't taken it very well.

Well, I'm one of those who haven't read it, so let's see what the article has to say about it.

What if I told you there was a paper on climate change that was so uniquely catastrophic, so perspective-altering, and so absolutely depressing that it's sent people to support groups and encouraged them to quit their jobs and move to the countryside?

Well, I don't have a real job to quit, but I can't get fast fiber internet in the countryside, so... hard pass.

"We're fucked," he told me. "Climate change is going to fuck us over. I remember thinking, Should I just accept the deep adaptation paper and move to the Scottish countryside and wait out the apocalypse?"

On the other hand, the Scottish countryside has one thing to recommend it. Well, two things, but mostly: scotch.

But most of all, there's the stark conclusions that it draws about the future. Chiefly, that it's too late to stop climate change from devastating our world—and that "climate-induced societal collapse is now inevitable in the near term."

I knew that without reading academic papers. Well, okay. I didn't "know" that. I suspected that. It's one of the reasons I chose not to have kids.

Look, the time to do anything about climate change was 30 years ago. Maybe even 20. Now? I just don't give a shit anymore.

Back in 2017, even Fox News reported scientists' warnings that the Earth's sixth mass extinction was underway.

Yeah... knowing Fox News, they reported it with a smirk and went on to extol the virtues of tax cuts for the wealthy.

He minces his words even less in his paper: "When I say starvation, destruction, migration, disease, and war, I mean in your own life. With the power down, soon you won't have water coming out of your tap. You will depend on your neighbors for food and some warmth. You will become malnourished. You won't know whether to stay or go. You will fear being violently killed before starving to death."

This is my shocked face:

Climate gloom and doom is nothing new—doomsday preppers have been stockpiling their freeze-dried food rations for decades now.

Fuck that. I wanna be among the first to go. Easier that way. In short:

As an aside, nothing makes me laugh harder than people who hoard gold against the possible collapse of civilization, no matter what the imagined cause. Come the inevitable, gold won't be worth the paper it's printed on; its value depends entirely on how shiny we think it is. "But, Waltz, gold has actual uses! It's a great conductor!" Yeah... that'll be helpful when nothing's generating electricity. No, if you're going to prep, the thing to hoard is coffee. It's not a domestic product in the US, and people are fucking addicted to that shit. Have a stockpile of freeze-dried, tinned, preserved coffee beans or grounds, and you'll be the King, Queen, Grand Nagus, whatever, of the Apocalypse. Possess gold, and people will just laugh. Other options include cigarettes and chocolate. Just be sure you can defend your hoard.

So, like I said, I don't care anymore. I used to. But decades of fighting denial, deflection and outright rejection have taken their toll on me. At this point, I'm just going to ride this sucker down with the hot wind in my hair and a grin on my face.

This is still the most fun slide to oblivion of any civilization, anywhere, and I've decided I'm going to enjoy the whirlwind.

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