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 5 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 18 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 21 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

about 23 hours 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

March 31, 2020 at 12:14am

#979755

Vive la Révolution!

Wrapping up entries for

Journalistic Intentions

[18+]
This is for the journal keeping types that come to PLAY! New round starts July 1!
by Elisa: Middle Aged Stik

Why the hell is this a video?

Let me get this out of the way. This video is over 20 minutes long and it's just a computer geek talking the whole time. Yes, he's good at talking. No vocal tics, few pauses, knows his material. Good for him. But I just wasted 20 minutes watching a video when I could have skimmed a written article and gotten the same outcome.

There are reasons to do video. This is not one of them. Its only saving grace is that it's not formatted vertically like savages do.

Techie Talk

I'm not an idiot, and I've been using computers since the late 70s. But I'm not in the business. I have no idea what half the shit he was saying was. Something about processor speeds and CPU architecture, none of which was really relevant to the point he's making. While it does serve to establish his geek smarts, I think I got the idea after the first phrase of tech jargon.

Rotten Apples

He opens with an analogy with totalitarian Soviet Russia, comparing the Apple user experience to that sort of propaganda cult. I find this especially amusing, because one reason Apple went mainstream was a S*per B*wl ad back in 1984 (long ago when I actually watched football), giving them an opportunity to draw parallels with Orwell. In it, a freedom fighter (supposed to represent Apple) destroys a propaganda film from the Establishment (supposed to represent IBM at the time).

I mean, really, that one ad is probably what started the S*per B*wl ad fad, as well as launching Apple into the consumer spotlight.

Here it is: https://www.youtube.com/watch?v=2zfqw8nhUwA

The text at the end of the ad: On January 24th, Apple Computer will introduce Macintosh. And you'll see why 1984 won't be like "1984."

So yeah, irony.

Same As The Old Boss

The problem with revolutions is, and has always been, that all they do is replace one kind of power structure with another. The replacement power structure might appeal to more people, but I guarantee you there were those who mourned the loss of the French aristocracy during the Revolution. At least briefly, until their heads were separated from their bodies.

I've known a lot of Apple fans, even from before 1984. Some of them are, as the author of the first video above noted, cult-like in their obsession. I understand, to an extent -- their products have always been more elegant, both inside and out. I never owned one of their computers, though, because it's always been easier for me to game on the Windows boxes. But I used them for years; my first career boss was an Apple fanatic. But those machines couldn't run AutoCAD worth a damn, either.

Point is, for me it's a matter of picking the right tool for the job. When I wanted a music device, I picked an iPod, not a Zune. I still use it; I don't trust streaming to not take my music away from me.

And I don't listen to Apple fanboys trying to shame me for using a PC. For fuck's sake, it's just another company.

Just Another Company?

Well, okay, it's pretty much the archetypal company. Their propaganda machine works better than their actual machines, as our intrepid geek above pointed out. This gives them staying power, despite the efforts of their detractors.

I like to point out that Steve Jobs started a company, with a couple of other guys of course, in his garage, and at the time he died, it had grown to be the most valuable publicly traded company in the world by market capitalization, surpassing not only Microsoft but such venerable giants as ExxonMobil and GE.

They're not that, at the moment, but that doesn't matter; the point is that now the revolution is long over and Apple is the Establishment.

2 Like • Comment • View 2 comments

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