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, Stik-or-Treat

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 Boris sent me

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 Boris sent me

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 Waltz in the Lonesome October?

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 Pumpkin

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 Howling

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

February 13, 2019 at 12:38am

#951885

Resurrection

Somehow, I managed to delete my entire bookmarks folder dedicated to blog fodder.

In the grand scheme of things, this isn't exactly Ragnarok, but it still pisses me off an inordinate amount.

I could find no way to recover the 35+ links I'd been saving to (mostly) rant about here.

I will allow myself five minutes to properly rage about this.

... ... ... ... ...

Okay, I'm done. Such are the ephemera of online existence. I did remember the last link I added, so that's what we're going to discuss today.

https://longreads.com/2019/02/11/atlantic-city-is-really-going-down-this-time/

Atlantic City Is Really Going Down This Time

There’s no doubt that Atlantic City is going under. The only question left is: Can an entire city donate its body to science?

Now, the site is called "longreads" for a reason, though I found the article worth reading. But I understand if you don't take the time to peruse it. Here's the tl;dr summary:

Atlantic city is boned because of flooding and the casinos that are popping up everywhere along the Northeast Corridor, and they're trying to turn the place into a climate science laboratory.

First let me say that this isn't an opening to debate climate change. Keep that shit on Facebook. I promise you that if you're not a climate scientist, you have nothing meaningful to contribute to the discussion on either side - and I'm not a climate scientist, either. No one's going to change their mind. This is about Atlantic City.

I've said this before, but I don't know where, so I'll risk repeating myself: I've been to Vegas, Reno, and Atlantic City - the major gambling cities throughout all my adult life. Vegas is Vegas; there's nothing else like it in the world, but it has its own problems in the form of Lake Mead being perennially low these days. Reno is so depressing they had to bring Morrissey in to cheer it up (I'm not kidding; the first time I was in Reno I saw a billboard advertising a Morrissey concert). And Atlantic City makes Reno look like Disney World.

The article speaks of a "duopoly" of gambling hubs between AC and LV, but I think they're giving Reno the short stick in that regard; Reno is even bigger than AC, but perhaps it is that city's relative proximity to Vegas that makes them leave it out. It's not even really that close, though - but it's one of my favorite drives, 8-9 hours through mostly empty desert, with the occasional ghost town along the way.

When I first went to a casino in Atlantic City, one of the slot machines there was Monopoly-themed. This amused the hell out of me, as it is well-known that Monopoly was based on Atlantic City's streets, railroads, and other features. The guy who invented it lived there, so the story goes, and made it up to keep him busy during the Great Depression.

Irony is thick on the ground, there.

That casino is now closed, along with several others, and the ones that remain have... issues.

So it will be interesting to see if the place can once again reinvent itself. While I have no moral issue with gambling, I will note that the more desperate a casino destination is, the harder it becomes for them to make a profit; consequently, games become stacked even more in favor of the house. And, as we've seen, in some cases, it's still not enough. They become less about entertainment and more about gouging visitors. Atlantic City is pretty damn desperate.

And yet, take away the glitz and the blinking lights, and it's an interesting little beach town. I'm kind of hoping they do find something to keep them going, before it, too, becomes just another ghost town.

Well they blew up the chicken man in Philly last
Night now they blew up his house too
Down on the boardwalk they're gettin' ready
For a fight gonna see what them racket boys can do

Now there's trouble busin' in from outta state
And the D.A. can't get no relief
Gonna be a rumble out on the promenade and
The gamblin' commission's hangin' on by the skin of its teeth

Everything dies baby that's a fact
But maybe everything that dies someday comes back
Put your makeup on fix your hair up pretty and
Meet me tonight in Atlantic City

Well I got a job and tried to put my money away
But I got in too deep and I could not pay
So I drew what I had from the Central Trust
And I bough us two tickets on that Coast City bus

Everything dies baby that's a fact
But maybe everything that dies someday comes back
Put your makeup on fix your hair up pretty and
Meet me tonight in Atlantic City

Now our luck may have died and out love may
Be cold but with you forever I'll stay
We're goin' out where the sand's turnin' to gold
So put on your stockin's 'cause the night's getting' cold and maybe everything dies
That's a fact but maybe everything that dies
Someday comes back

Now I been lookin' for a job but it's hard to find
Down here it's just winners and losers and
Don't get caught on the wrong side of that line
Well I'm tired of comin' out on the losin' end
So honey last night I met this guy and I'm
Gonna do a little favor for him
Well I guess everything dies baby that's a fact
But maybe everything that dies someday
Comes back
Put your makeup on fix your hair up pretty and
Meet me tonight in Atlantic City

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