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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Turkey DrumStik

about 7 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

November 13, 2018 at 1:20am

#945463

Excelsior!

If you do what you really want to do, you feel like you're playing. - Stan Lee (1922-2018)

Stanley Martin Lieber wanted to save his real name for literature, so when he got started writing the supposedly lowbrow stories for which he'd later become famous, he used the pseudonym we've all come to know well.

As I've said before, I've always hated the term "genre fiction," and I never use it. It's intended, I think, to distinguish fantasy, science fiction, horror, supernatural and other stories from "literature." But all stories have a genre - some, more than one. I noticed that yesterday's science fiction, fantasy, etc. become today's literature - Mary Shelley, Poe, Twain, Stoker, Verne, Wells, Burroughs, etc., and I saw no need to wait for time to pass so that others could appreciate fiction with otherworldly elements the way that I did.

When I was a kid, I tried reading comics, and I tried reading The New Yorker. The former stuck. The latter... well, I figured when I got older, I might understand and appreciate that magazine's post-modernist, rambling, allusion-laden, snobbish style.

I never did.

I did like the cartoons, though.

Comics are a strange blend of genres - so much so that they have become a genre of their own. From the outset, which for the sake of argument I'll place at the first publication of DC's Action Comics 80 years ago, they have always blended science fiction and fantasy. I've mentioned in this space and in newsletter editorials that I have problems with stories that get the science wrong. Boy, do comics get the science wrong - but the best of them are internally consistent; hence the fantasy aspect.

They are, you might say, modern fantasy; or, as I prefer, modern mythology, the stories of those with powers far beyond those of ordinary men and women. Gods, in a sense - gods who walk among us. Or fly. Or teleport. Or run really, really fast.

Even those comic book heroes without identifiable powers have honed their skills in ways that make them greater, but whether human, alien, mutant, or irradiated, most of them share one trait: the desire to do good, even if the heroes themselves are just as flawed as we - or their creators, writers, and artists - are.

They urge us to become the best that we can be.

Apparently, for me, the best that I can be includes an abiding love of comics: in their original words-and-pictures format, in their TV and movie adaptations, in books, in behind-the-scenes interviews. I guess you can call me a fanboy, even if I've never dressed up as Spider-Man or gone to a comics convention (I have been to general F&SF conventions, but none of the big Comic-Cons).

These past 10 years or so - the time since Marvel's Iron Man first exploded onto the big screen - have seen a renaissance of comics adaptations. Some people are tired of that. I get it - it's not everyone's vial of super-serum. Comics movies were made before 2008, though, and will continue to be made until they're no longer making money for the studios, which probably won't be anytime soon. Personally, I'm tired of rom-coms, but my solution to that is to simply not go see them. Problem solved.

I can say with some certainty that if it weren't for comics, I wouldn't have had the urge to write, or to appreciate science (even if the latter was out of the curiosity to see just how bad they did science). I wouldn't be the person that I am.

I never did get a taste for The New Yorker's snobbery, but look at this:

https://www.newyorker.com/news/daily-comment/black-panther-and-the-invention-of-...

That's an article in the most snobbily literary of art-snob magazines post-modernistically deconstructing a movie based on a comic book character co-created by Stan Lee - and unabashedly praising the film.

And the man - The Man, as he was known - lived long enough to see his "lowbrow" life's work join the ranks of literary fiction in being analyzed, scrutinized and reviewed by that magazine, and in a positive manner at that.

So if you're wondering why so many people are reminiscing on this one guy's life today, well, it's because he's one of the people who actually changed the world for the better, inspiring millions of people and adding to the world's body of great literature.

Not bad for a pulp fiction writer.

(Note: I'm probably going to crib heavily from this entry for next week's Fantasy newsletter, so if that editorial seems familiar, that's why.)

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