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

December 22, 2007 at 8:38pm

#556663

Solstice Day.

Shortest day of the year? Big fucking whoop. It was as cold, cloudy, dark and dreary as a Morrissey song.

I wasn't going to go anywhere today; I was just going to sit on my ass or lie in my bed and celebrate the first of many days off in a row - and, of course, put together next week's Comedy and Fantasy newsletters, which are now almost done.

But my cunning plan was foiled.

There was not a single can of Coke Zero in the entire house.

Now, given a choice, I'd be drinking real Coke. But since they started making it with corn syrup instead of sugar, it just hasn't been right. So as long as I can't get the real stuff, I might as well bow to the low-calorie ideal and get the Zero, which tastes a hell of a lot better than Diet Coke, which in turn is ambrosia compared to anything made by Pepsi.

But if there had been nothing in the fridge but a Pepsi, I'd have drank it, merely because it contains caffeine.

Oh, but Waltz... what about coffee? You ask. I know you're asking. I can hear you. Well, as lousy as that crap Pepsi is, it is sweet nectar compared to coffee. I've never developed a taste for coffee, and I've never yet been desperate enough to need some. Consequently, there's none in my house, which brings us back to my main point...

Caffeine addiction is a real thing. I don't know about anyone else, but upon withdrawal, I get irritable, cranky... okay, MORE irritable and cranky, and on top of that I get this headache that nothing can fix.

Nothing, that is, except drinking something with caffeine in it.

I did, briefly, contemplate making myself a cup of Earl Grey, but for me, the hotness of tea cancels out any caffeine molecules it might have. Nope, there was only one cure for my splitting headache, and that was to go get some soda.

So it was off to the Food Lion (sometimes known as Fool Dyin') to get some Coke Zero.

When I got there, the first thing I saw after all the bedraggled, harried customers and the tired, foaming at the mouth checkout people was that there was no Coke Zero in the refrigerated sections.

Okay, no problem. Diet Dr. Pepper works just fine. So it's a 20 oz DDP and two (on sale!) 12-packs of CZ. Oh, but while I'm here I'm also going to get a bag of pretzels and a box of nukable popcorn!

So much for the advantages of low-calorie soft drinks. This is why I usually get my wife to shop for me. Well, that and I'm lazy.

Anyway, the story ends well - I chugged the DDP and within minutes my headache had resolved into a low roar, once more taking second place to the sharp, stabbing, radiating, numbing, tingling, unbearable pain in my lower back. A pain, in short, that no amount of caffeine can fix, but at least I don't have that godawful damn headache anymore.

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