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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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 15 hours ago
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

about 22 hours ago
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

a day ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

a day ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

Dec 26, 2024 at 10:00am
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

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.

4 Like • Comment • View 3 comments

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