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:

Write_Mikey_Write!

about 15 hours 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

about 17 hours 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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

April 7, 2020 at 12:11am

#980425

National Beer Day

Today is one of my High Holy days.

Well... truth be told, I just found out about this important day for the first time, but it immediately went on my list of important things to commemorate, right up there with the December 5 ratification of the 21st Amendment.

And it's related. The 21st, repeal of Prohibition, was passed in 1933. But before then, the legal limit for beer was raised from 0.5% to 3.2% ABV

, so this is a beer-specific observance. Plus, as the link above can attest (insofar as one can trust Wikipedia), this Holy Day got its start right here in Virginia.

So as soon as I post this, guess what I'm going to do. Go ahead. Guess. That's right -- have a beer.

This is a good time to segue gently into today's random feature article.

https://theconversation.com/how-steak-became-manly-and-salads-became-feminine-12...

How steak became manly and salads became feminine

When was it decided that women prefer some types of food – yogurt with fruit, salads and white wine – while men are supposed to gravitate to chili, steak and bacon?

And beer. Somehow, wine became a chick thing while beer became a dude thing. Fortunately, there's not much social pressure to conform to these idiotic genotypes (a word that means something else but I've claimed for this definition now), not like there is with the difference between soft, fruity mixed drinks for chicks and hard bourbon for dudes. I say fortunately, because while I talk about beer a lot in here, and I do love me some craft beer, I'm also an inveterate wine snob. And a gin snob. And a tequila snob. And a rum snob. And a whiskey snob... you get the picture (vodka I don't give a shit about, though I'll drink it).

In my travels to various breweries, wineries, cideries, and distilleries, I have noticed some gender segregation, but not as much as pop culture would have you think. In truth, all booze is gender-neutral.

But back to the food thing.

In my new book, “American Cuisine: And How It Got This Way,” I show how the idea that women don’t want red meat and prefer salads and sweets didn’t just spring up spontaneously.

Yeah, this writer is shilling a book. Again, this is a site for writers, and I don't begrudge anyone the opportunity to promote their book, especially if, in the process, I get to read a somewhat interesting article and share it.

It was during this period that the notion that some foods were more appropriate for women started to emerge. Magazines and newspaper advice columns identified fish and white meat with minimal sauce, as well as new products like packaged cottage cheese, as “female foods.” And of course, there were desserts and sweets, which women, supposedly, couldn’t resist.

As with everything else, it seems, marketing rules the day.

The 20th century saw a proliferation of cookbooks telling women to give up their favorite foods and instead focus on pleasing their boyfriends or husbands. The central thread running through these titles was that if women failed to satisfy their husbands’ appetites, their men would stray.

Look, ladies, your man's going to stray anyway. He can't resist it, any more than you can resist "desserts and sweets." ... well, at least that's what marketing has pounded into us.

Even in the 21st century, echoes of cookbooks like “The Way to a Man’s Heart” resound – a sign that it will take a lot more work to get rid of the fiction that some foods are for men, while others are for women.

As with most gender stereotypes, the only way to resist it is to reject the pounding of marketing, and be immune to social shaming. I eat salad when I want to. Never appreciated cottage cheese too much, but I do like yogurt, another food generally marketed to broads. And I happily drink wine, be it white, red, or rose. While there are probably some differences in nutritional needs between the sexes, in a very general sense, I have my doubts that they're as sharply divided as marketing makes them out to be.

And now it's Beer Day.

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