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

Stik to My Own Beat

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 wanderlust-words-in-motion

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 wanderlust-words-in-motion

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 Surprised

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

November 17, 2010 at 10:09pm

#711689

On A Jet Plane

So there have been a good number of stories lately about airport screening measures, revolts upon same, and lawsuits.

Here's one:

http://www.prisonplanet.com/tsa-hit-with-lawsuits-as-revolt-explodes.html

Now, this got me to thinking, because I find myself once again planning air travel (this might be my last flight unless sanity resumes).

One complaint I've heard is that you can either walk through a scanner that essentially takes a naked picture of you through your clothes, or opt for a physical scan. The latter involves someone groping your privates (and I somehow doubt that someone looks like Zoe Saldana, or I'd totally fly more).

Now, honestly, I'm of two minds about this. While I think the threat of terrorism is real, I also think it's blown (see what I did there?) way out of proportion. Here's an article from Cracked that elucidates it pretty well:

http://www.cracked.com/article_18849_6-statistically-full-s2321t-dangers-media-l...

Summary: Cows are more hazardous than sharks; stairs will kill you before elevators will; and: "In the last decade -- including the 9/11 attacks -- you've been about 10 times more likely to die from a fire you accidentally set in your home than from a terrorist attack. Somebody should make a show about a Jack Bauer type who runs around reminding people to put out the goddamned cigarette before they pass out on the sofa."

Now, you can argue that it's airport screening that keeps the incidence low. I'm not going to argue with that, because I don't have the data and I'm too lazy to look it up. All I know is, I think they could fucking ease off a little without significantly raising the chance I'm going to get blown up by a right-wing extremist or other terrorist type.

Hell, I don't see metal detectors installed around Detroit, and if you enter THAT shithole, you're taking a way bigger chance than you are flying.

Anyway, my other mind is like: Who cares? So someone can see my privates in an x-ray scan. We as a nation need to chill the hell out about nudity, anyway. We make such a goddamned big deal of it people are STILL talking about Janet Jackson's boob at the Superbowl from a few years ago.

Relax. It's a body. Half the people in the world have one similar to yours. Leaving aside whether the measures are actually useful or not, so what? Maybe there'd be less anger in the world if we could see each other naked more often. More disgust, maybe, but less anger.

So here's my proposal:

Everyone show up to the airport naked.

Seriously.

They're going to look anyway. And you can put your clothes in a carry-on and slip into them before you get on the airplane. They can look through your carry-on, but there'll be no damn reason to x-ray or grope you.

Just show up naked.

That's a protest I can get behind.

(See what I did there?)

Anyway, I also wanted to share this, which is completely unrelated:

We want to offer all of you an apology. We asked our readers to photoshop us some "inappropriate children's book covers." This seemed like such a simple, innocuous idea because quite frankly there is nothing as innocent as a child and there is no more wholesome activity than reading.

More than 400 entries later, we realized how tragically, horribly wrong we were. We have ordered the following entries roughly from least disturbing to most, and the very worst have been placed safely at the end. We recommend no one look at them.

At the very end we have placed the winner, who will receive five thousand pennies, which is $50. Again, we're sorry.

We apologize in advance for the eight most offensive entries, #8 to #1.

http://www.cracked.com/photoplasty_3_the-40-most-inappropriate-childrens-book-co...

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November 9, 2010 at 12:34am

#710794

Iconoclasm

So I went to Iowa over the weekend.

It's not what I'd call a short drive. Left Thursday. Spent Thursday night in a hotel in Indianapolis.

I've decided I don't like Indianapolis, but that's a discussion for another time.

Went through all the "I" states, in fact (except for Idaho, into which I'll probably never set foot) and ended up at a sf/fantasy convention in Cedar Rapids. The convention was called iCon; hence the title of this entry.

Yes, this was planned. I hung out with Storm Machine

over the weekend. She's pretty cool. And her friends are weird. But cool!

A few notable things:

1) Time changes suck. Gained an hour crossing into Illinois. While I was in Iowa, DST ended and I gained another hour. On the way back, crossing back into Indiana, lost an hour. I'm still not sure what time it is. Not sure I really care. No, I'm not a fan of the band Chicago.

2) Illinois has vineyards. What the fuck?

3) The Mississippi River is way wider than I thought along the Illinois/Iowa border. I mean, it still has a thousand miles to go before it hits New Orleans. I'm sure everyone else knew this already, but this weekend was the first time I've ever crossed that river in anything but an airplane.

4) Does any state (besides Virginia) NOT have casinos now? Are we that desperate? Really?

5) I can still drive 10 hours at a stretch.

6) But not much more than that. Sunday I stopped outside Columbus because Brandiwyn🎶Prep starts 10/1!

and her boyfriend were kind enough to put me in their guest bedroom for the night (THANKS!). She said she'd wake me up at 8:30. 'Round about 11:30 (I think - time shifted a lot this weekend) I stumbled out of bed.

7) When a pigeon commits suicide on the front of your brand-new car, it leaves a pigeon-shaped silhouette, just like in the cartoons.

8) Iowa isn't NEARLY as flat as advertised. It does, however, contain cornfields. No Enterprise drydock, though, sadly.

Next stop on the Waltz World Tour: Las Vegas, next month.

Think I'll fly, this time...

Comment • View 6 comments

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