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!

about 9 hours ago
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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.

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Adherennium Plotting something

about 11 hours ago
In response to "Global Domination"

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

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Brandiwyn🎶

Nov 12, 2024 at 10:50am
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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.

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Turkey DrumStik

Nov 8, 2024 at 9:47am
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Lilli 🧿 ☕

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

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February 3, 2024 at 10:38am

#1063374

Burgundy

For "Journalistic Intentions"

[18+]...

Burgundy

Not all red is burgundy, and not all burgundy is red.

Burgundy (the region in France) apparently has a long history of influence in Europe. I've heard that, for a while, it was Burgundy (Bourgogne in French) that was the cultural center, not Paris. All things rise and fall, though, and now the region is mostly just famous for wine.

And mustard. Yes, mustard; the capital of the region was once also the capital of mustard-making. The capital's name is Dijon.

But while mustard's a fine condiment, I'd rather talk about wine.

As with most wine-producing regions, they grow a wide variety of grapes there. Many of them produce red wine. Many others produce whites.

Last November, I did an entry about one of my favorite French wines: "Beaujolais Nouveau Day"

. Now, the Beaujolais region is just south of, and adjacent to, Burgundy. Incidentally, these blog entries are inadvertently helping me plan a trip to France. Anyway, point is, Beaujolais grapes grow in Burgundy, too.

But Burgundy is responsible for what I consider to be the light beer of the wine world: Chardonnay.

Unlike light beer, though, Chardonnay doesn't suck. It's just... everywhere. It's often the entry port into the land of Oenophilia. Those grapes can apparently grow just about anywhere, which means most of the wineries I've visited have some variation of Chardonnay. Now, I'm not ragging on peoples' tastes; if you like it, you like it, and that's fine. But there are so many other whites, including many from Burgundy, just waiting to be tasted. Like Pinot Blanc, also Burgundian, though better examples can be found elsewhere.

And yet, the region is most known for its red wine, to the point where an official name for a certain shade of red, possibly reminiscent of the ruby color of a red wine, is called burgundy.

Burgundy (the color) is quite similar to bordeaux (the color), though Bordeaux is an entirely separate wine-growing region, located on the Atlantic (west) coast of France. Unlike Burgundy, Bordeaux is better known as a wine region than as a color, to the point where I've taken to calling all boxed wine "cardbordeaux."

I'll have to remember not to use that word when I'm in France. I've heard the people there can be... a bit touchy about certain things.

So, to reiterate: not all red is burgundy, and not all burgundy is red.

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