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 21 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 27, 2024 at 11:32am

#1064998

Olive It And More

To wrap up February's "Journalistic Intentions"

[18+]...

Olive

There's a grocery store on Broadway, on the Upper East Side (corner of 80th Street if you're ever in the area) called Zabar's.

I get the impression that it's moderately well-known across the land. Maybe it's been in a movie or show or two; I don't know. Maybe its vibe, which more modern and chain-affiliated places can't replicate with their corporate policies, focus on metrics, and eventual enshittification, is just something people respond better to.

Since I haven't been there in a while, I can't comment on their prices, but I remember them being about what you'd expect in Manhattan: slightly elevated, though not sky-high like in Hawai'i. But their location means they serve a moderately well-to-do clientele, which means offering some premium selections. The first time I went in there, I nearly dehydrated salivating over the seemingly endless, though really not because we're still talking about a Manhattan grocery store with limited space, selection of cheeses.

And then I saw the olive section and almost fainted from delight.

I like olives, you see. Not just black, green, and kalamata, but all olives.

Want to hear my most idiosyncratic quality? I don't think I've ever admitted to it in here before. Or anywhere online, really. I usually keep it to myself, because the one time I told someone in person, the look I got was so filled with horror and disgust, you'd think I made a habit of munching on baby sandwiches.

I get green olives on my pizza.

That's right. Pizza. New York slice, of course, with, at minimum, pepperoni and onions... and green olives.

I can't be alone in that, even if no one else will ever fess up. If I were, the local pizza shop wouldn't offer it as a topping, would they? And not just the local pizza shop, but the old one, the one that had been around since before I even got to town in 1983, the one that even more closely approximated NY pizza but sadly went out of business because of, well, you know—they offered green olives on their pies, too. Not just because of me, either; it was on the menu when I first visited each of them. Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives. But usually, they get it right, and they've never been out of stock (to be fair, the whole reason for green olives is preservation, so the little eyeballs might have been sitting around for years, for all I know).

Last time I went to pick up my extra cheese-pepperoni-onion-beef-jalapeno-green olive pizza at the place that managed to stay open, I recognized the owner as the one who provided the pie to me. "Ah, good! Green olives!" he enthused in his boisterous, Brooklyn-Italian accent. "You have wonderful taste!"

Finally, vindication.

1 Like • Comment • View 1 comment

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