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:

🌝 HuntersMoon

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa, Snowman Stik

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pon

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

1 Like

BIG BAD WOLF is Merry

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

January 24, 2008 at 4:54pm

#563117

Wavering

I've been trying to think of something to say today; preferably, something innovative, honest, revealing, self-deprecating and more than a little funny, since that sort of thing seems to draw in blog readers - but I can't seem to pull any bumper-stickers out of my hat, these days.

I didn't want to resort to another day of weird news stories, though I have a couple I'd really like to post - only one of which involves Hello Kitty. They can wait.

Sadly, the big news today seems to be the "economy stimulating package" or some such from Washington, which apparently does to us what the government always does to us - stick their package to us in a stimulating (to them) manner, over and over again. If I were a politically-inclined blogger, I'd link a serious article on it from a serious news source, like this one:

http://www.washingtonpost.com/wp-dyn/content/article/2008/01/24/AR2008012400532....

In case you can't read it, I'll summarize:

Nancy Pelosi and John, A Boehner (a setter and a pointer, respectively) worked late into the night trying to find different means of stimulation, rejecting trickle-down schemes in favor of something similar to the Bush stimulation a few years back, wherein almost everyone gets some (unless you're wealthy, in which case you're already getting some). This isn't meant to shaft Americans so much as stroke them, convincing us to spend ourselves into exhaustion. Seems like quite the opposite of the trickle-down theory - I'll call it the "spurt" theory of economics where the flow is from the "bottom" of the economic frenzy to the "top," from which it just might drip back down again.

So it seems we can expect the package (which Bush said was "just the right size") to climax sometime in May. It'll most likely be spent quickly. Then the government can roll over and go back to sleep, leaving the people blinking at the ceiling, frustrated and wanting more despite the frenzied activity of mere moments before.

...But I decided that to comment at all upon such trivialities is beneath me; first, because I'm not a politically-inclined blogger; second, because you'll have heard all about it already and formed your own opinions; and, finally, because it lends itself too easily to parody, and I'd never stoop so low.

Then I thought that maybe I could present to you my latest forays into the philosophical world, especially as regards the meaning of life, the Universe and everything; the difference between reality and illusion, with an emphasis on why it is that so many people find deep comfort and meaning in the belief that reality is an illusion (with commentary on how difficult people like that are to deal with); and the general banality of things like economic stimulation packages. But when it comes to philosophy, I really don't know what I'm talking about. I mean, apparently, those things that I think are real - like trees, flowers, the past and concrete - are actually abstractions, illusions formed by my mind to distract me from the real, true reality, while those things that are illusions to me - like dreams, fantasies, the future and story ideas - are, to these same people, the true reality that I should be focusing on. Worse still are the "forget the past, ignore the future, live only for the present" types, most of whom have credit card debt that make many small countries jealous. But it's been made clear to me that I don't know what I'm talking about on that score, and besides, it takes too much effort to type anything on this illusory keyboard - especially anything about the past, which they've already established as illusion that can be disregarded, but to me makes for the most engaging writing (after all, you can't write about the present - because by the time you've written about it, it's the past).

I mean, seriously - how shitty does your past have to be for you to make like it's not real?

But I'm not going to go there.

I guess I'll have to post the Hello Kitty link after all.

But first, the Idiot Test. Take it and see how far you can go with it:

http://users.skynet.be/bk258512/idiot_test.swf

And now, the Nefarious Neko herself:

http://www.hellokittyuniverse.com/page/Indecent%20Hello%20Kitty%20Products?t=ano...

Oh. That's why people have to claim everything is an illusion. It makes the prospect of Hello Kitty Menstrual Pads that much easier to take if you can keep saying to yourself, "It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away..."

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