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

July 28, 2008 at 3:28pm

#598960

Burgers and Beer

Everyone knows that burgers and beer constitute a man's perfect meal. I mean, if I were about to be executed for my political beliefs and they offered me a last meal, I'd be like, "Burgers and beer, please."

But there IS a such thing as taking things too far, like these abominations of all that is right and good in the world:

http://www.diet-blog.com/archives/2008/07/21/the_7_hamburgers_of_the_apocalypse....

Hamburgers, next to apple pie and statins they're the ambassadors of American cuisine--for better or for worse--and these harbingers of heart disease might be the baddest of all.

Here are 7 over the top hamburgers that are guaranteed to clog your arteries by just looking that them:

I mean, why don't you just slit your wrists and jam the burgers directly into your veins? It'd be quicker and less painful.

And I thought the Krispy-Kreme Bacon Double Cheeseburger was bad. Hell, even if I weren't severely curtailing my burger consumption in the process of overall weight loss, I wouldn't be able to come anywhere near such dread concoctions.

But the news is better on the Beer front. It seems that people are finally starting to catch on to the knowledge that Buttwiper isn't beer. Neither is Miller or Coors, and don't even get me started on the "Lite" versions.

http://www.time.com/time/business/article/0,8599,1826878,00.html

High-alcohol brews like Black Butte XX and The Abyss, known in the trade as big or extreme beers, are among many craft beers that are grabbing a growing market share in the United States from their mass-produced and heavily advertised counterparts. Even at prices ranging from $4 to more than $100 for a single bottle.

Well, DUH.

Sales of premium beers, which include the household names of Budweiser, Coors Light and Miller High Life, have been nearly flat — up just 1.9% last year according to Information Resources Inc., a retail research firm.

Sucks if you've got stock in Buttwiper. Or whatever they call it now that it's a Belgian company. And what's up with that, anyway? Belgium makes the best beers. Delirium Tremens, for example. Holy shit, I'm getting drunk just thinking about DT.

Oh, yeah, I know beer isn't exactly helping with the aforementioned weight loss. But what's the point of being thinner if you can't drink beer? It just ain't worth it.

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