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:

Elycia Lee ☮

about 7 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 ✍️

about 20 hours 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

about 23 hours 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

a day ago
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

a day ago
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🎶

a day ago
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

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

February 6, 2020 at 3:09am

#974958

Come the Revolution...

For various reasons, I decided to get completely drunk yesterday. Then I came home and passed out; hence the relatively late entry today.

https://www.fastcompany.com/40467032/the-end-of-capitalism-is-already-starting-i...

The End Of Capitalism Is Already Starting–If You Know Where To Look
One of America’s foremost Marxist economists has never felt so optimistic in his 50-year career.

Americans like to think everything is binary. You're either an alcoholic or a teetotaler. Anyone who's not vegan is a murderer. If you're not a Republican conservative, you're a liberal Democrat. That sort of thing. But reality isn't binary; it's spectrum - so the choice isn't "capitalism" or "socialism" but any number of in-betweens.

Over the summer, inequality experts Jason Hickel and Martin Kirk launched a conversation on this site when they posed the theory that capitalism is at the core of the many crises gripping our world today.

Actually the core of the many crises gripping our world is that there's too many people on it. But every time someone points that out, someone else goes, "So go ahead and kill yourself, then." If enough people urge me to do so, I probably will, so I'm not going to dwell on the too-many-people hypothesis.

“Americans are getting closer and closer to understanding that they live in an economic system that is not working for them, and will not work for their kids,” Wolff says. Growing awareness that wages have been unable to keep up with inflated costs of living have left younger generations particularly disillusioned with capitalism’s ability to support their livelihoods, Wolff says, and with CEOs out-earning employees by sometimes as much as 800 to 1, it makes sense that public interest should be swinging toward a workplace model that encapsulates shared ownership, consensus-based decision making, and democratized wages.

Which is one reason I didn't have kids.

Also, I mean, that has been completely obvious to me for a long time, so obvious that it went without saying: instead of "management" and "unions," why not have workers with a stake in the company? Again, non-binary.

“The image of the transition from feudalism to capitalism was the French Revolution, and that was part of it,” Wolff says, “but it wasn’t the whole story. The actual transition was much slower, and not cataclysmic, and found in these serfs that ran away and set up something new.”

A friend of mine is fond of sending me gifs of guillotines whenever some super-rich capitalist shithead does something to fuck the rest of us over. While I owe my existence and all of my luxuries and luck in life to capitalism, I can't say I disagree.

Anyway, I didn't link this article because I agree or disagree with it; again, life isn't binary, and I don't feel the need to fling myself to one side or the other. As with science, I just find it fascinating and worth watching. It's something to think about, especially if you're trying to find a decent job and health insurance in today's "booming" economy.

3 Like • Comment • View 2 comments

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