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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🌝 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.

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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

May 23, 2008 at 3:28pm

#586743

Memorial Day Weekend

It's Friday, the last day of work before a long Memorial Day weekend, so I thought today I'd talk about what this weekend is all about:

Drinking.

Yes, I'm in a slightly better mood, so I'm starting to feel the urge to, as I put it a couple of days ago, consume vast quantities of alcohol.

I'll start tonight at Chili's. Now, Chili's is a lousy chain, but they do have one thing that's worth ordering: the Presidente Margarita. Oh, sure, it's watered-down, and I won't ask what tequila's inside it, but it comes in this shaker that they pour into an iced, oversized martini glass with a salted rim. The shaker's usually good for three or four pours, after which one must order another one.

Kirstin is going away for the weekend on a camping trip. Good for her. I'd kill myself after about an hour of "roughing it," and then she'd have to clean me up from her brand-new pavilion tent. No, I'm going to stay home and drink.

I have, in the fridge, a bottle of Vouvray (an excellent white wine from the Loire valley of France). I'm thinking since Saturday's supposed to be nice, I can spend part of the afternoon drinking it out on the deck. Then, when my ex-wife calls for me to help her out of some Jerry Springer situation, which she continues to do even to this day, I can honestly say, "Nope. Can't drive. Call someone else. Oh, wait, you've exhausted your supply of friends and that's why you're calling me? Bummer." And then I can proceed to drink some more.

If I run out of Vouvray, I have a few bottles of Magic Hat #9 left in the fridge. If I get really desperate, I'll drink the two bottles of Bud Light I keep in there on the off chance Pat visits me. If I get completely desperate, the nearest grocery store is within staggering distance. Come to think of it, the nearest bar is just a bit further away, in the other direction. It'll be interesting to see which one I choose if I've got a good drunk on. The only thing I can guarantee is I won't be driving; I'll be drunk, not stupid.

But even if I decide that staggering a mile each way in the evening isn't really for me, I've still got most of a bottle of Magellan gin, and olives and dry vermouth - or even tonic water. Hell, by that time, my mostly-full gallon bottle of Cuervo Gold might start looking good.

Sigh.

Yeah, all that sounds good now, but the fact is I don't like to be out of control or having the room spin around me, so the reality of it is I probably won't drink all that much. I can't enjoy what I usually do - reading, playing video games, working complicated math puzzles, or even watching a good movie or playing on the Internet - while drunk.

Hell, maybe I can even go see Indiana Jones or Speed Racer while sober.

No, scratch that. I'll need to be completely schnockered to go see Speed Racer.

Oh, and the thing about Memorial Day being all about drinking? I was being facetious. Do take some time to remember those who put themselves in harm's way to keep us (relatively) safe and free. I know I'll be raising one for my dad.

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