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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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').

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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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

June 8, 2019 at 12:51am

#960367

Where to Drink in Charlottesville

Make a listicle (list-article) of the Top 10 things to do in your area as a tourist

In old-school David Letterman fashion, I'm going to do this as a countdown.

As regular readers know, I live in Charlottesville. Used to be, I'd have to tack the state on lest people think I live in Charlotte, NC. Nowadays, we've become a household word, right alongside 9/11 and Columbine.

This, frankly, sucks.

So without further ado, the Top 10 things to do in Charlottesville as a tourist.

10. Barboursville and Other Wineries

Our most famous resident, Thomas Jefferson, had an idea. Well, he had lots of ideas, and some of them were actually pretty good ones, like, you know, let's not be British anymore. This one in particular was this: the climate around Charlottesville is roughly similar to that of some parts of France. And what's France famous for? Guillotines, art, and wine. While the guillotine never quite caught on around here, and you can do art pretty much anywhere, Jefferson thought maybe we could grow wine.

It... didn't work out the way he hoped.

At least, not until around 1980 or thereabouts. Maybe a bit earlier. Some wine snob figured out a way to actually get wine grapes to grow here - well, close to here, anyway; in a little town called Barboursville about 30 miles northeast. The particular plot of land where the magic finally happened is also home to the ruins of a former governor's mansion, which was, by coincidence, fate, or planning, designed by Thomas Jefferson. It is, as I said, in ruins, having burned long ago, but the principal method of construction around here is brick, so the shell survives to this day. I got married there once. Anyway, point is, from that one winery, other people copied the idea (for wine, not burned-out ruins) and so we're home to the best vineyards outside of California and France.

9. Robert E. Lee on a Goddamn Horse

This hunk of bronze is what eventually made us world-famous. Which sucks, because, well, there's a lot of history here, history that involves people who actually have a connection to this town, like the dude who wrote the goddamn Declaration of Independence, founded the University of Virginia, and served as a motherfucking president of the actual US. City Council voted to remove it, but there are legal issues and the son of a bitch is still there. They tried covering it with a tarp, but that didn't work out so well. So you can still see it, if you hurry.

Now, look, Jefferson had his faults. So did Lee. So did Martin Luther King, Jr. Everyone does, especially if you judge the people of the past by the standards of the present. In 200 years, every one of us will probably be excoriated for owning a computer. That's not the point; the point is that the duly elected city council voted to remove the statue, and a whole lot of carpetbaggers descended upon our town in protest, leading to... unpleasantness.

8. The Rivanna Trail

Like to walk? The Rivanna Trail circles the city - and for most of it, you won't even know that you're in a city. I've never been on more than a short segment of it at a time, myself, because it involves being outdoors, and you know how I feel about that. But I featured it in a novel (that remains unpublished and in draft form), so I had to walk some of it. For research, you know.

7. South Street Brewery

This is an important historical landmark, as it was the first microbrewery in Charlottesville. It is where I discovered what real beer was. While it's changed hands a couple of times, it still makes excellent beer and is worth a visit. Their food is pretty good, too.

6. Miller's

Charlottesville's downtown is dominated by an outdoor [shudder] pedestrian area, converted from a street, called the Downtown Mall. The whole mall is worth a look, but for visitors, Miller's is important because it's one of our oldest bars, and Dave Matthews used to sling "beer" there. Hey, I know - let's put up a statue of him! Horse optional.

5. University of Virginia

Now forever to be known as the site of the Tiki Torch March, it's worth a visit if only to assure yourself that we don't usually have Tiki Torch Marches. They teach stuff there too, sometimes.

4. Monticello

I debated with myself whether to include this most touristy of tourist places in (or, rather, just outside of) Charlottesville, eventually opting to do so because to exclude it would be like leaving the Eiffel Tower off of a list of tourist things to do in Las Vegas. Er, I mean, Paris. Or omitting the Statue of Liberty from a list of tourist things to do in Las Vegas. Er... New York. Whatever.

3. Carter Mountain Orchard

On your way to or from Monticello, go up a winding-ass paved driveway to the top of Carter's Mountain. The views are incredible, and they have hard cider. Hm, I'm noticing a theme here. Now, people from out west might look at this "mountain" and scoff, but at least we have mountains people can hang out on without passing out from lack of oxygen. Cider, maybe, but not lack of oxygen.

2. Gearhart's Fine Chocolates

Located near the Downtown Mall, I've been assured that they make the best chocolate in the country. Possibly even the world, but I will have to wait until I go to Belgium to determine this for myself. Strictly for research purposes, of course.

And the Number One thing to do in the Charlottesville area as a tourist (drumroll)...

1. Go Home.

I moved here when I went to UVA, then stayed after graduation, but I've lived here long enough now that I can say this.

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