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:

Turkey DrumStik

about an hour ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

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

3 Like • Comment

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