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 8 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 10 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').

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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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

July 23, 2020 at 12:02am

#988913

Butcher

Well this is a little less controversial than yesterday's prompt, but not much so.

PROMPT July 23rd

You've been given a full budget and creative license to bring a book you read to film. What book would you pick and who would you cast as the characters? If you choose a book with an existing movie adaptation, what changes would you make?

Plenty of books I could choose, but I'm going to go with the one I most recently read. Or actually the entire series of books, which is up to 16 now (soon to be 17). Also, I'm loosely interpreting "film" here; the line between movie and TV series is getting blurrier all the time, and with 17 books you need it to be a series.

I'm talking about Jim Butcher's Dresden Files, which has been going on for 20 years now.

SyFy (or, well, I think it was still The SciFi Channel at the time) did a short-lived series adaptation in 2007, but as far as I'm concerned that doesn't count. I've never seen it, anyway. So I'm ignoring it for these purposes.

For anyone who hasn't read the books (and you should, because one of them contains the greatest scene in all of literature), Harry Dresden is a wizard who lives in Chicago and gets himself into supernatural trouble on a regular basis, consorting with vampires, werewolves, faeries, etc. I figure since the show Supernatural is ending, this could fill the void with something actually, you know... good. The books combine elements of contemporary fantasy, noir detective, and comic book tropes.

Now, here's one problem for casting: time passes in the books. That is, the Harry Dresden from Storm Front is about 20 years younger than the Harry Dresden from the latest book, Peace Talks. So you either have to grab a 30 year old actor and age him up something close to naturally, or cast anyone and use de-aging tech, which has come a very long way in recent years. You did say "full budget," though, so I'm not letting age get in the way. Also, 50-year-old actors are going to be better known to me than 30-year-old actors. To complicate matters, some of the characters are supernatural and don't age much if at all. (The Witcher has this problem too.)

The most important character is, of course, Dresden himself. The books are written in his first-person point of view. I considered Henry Cavill, but he's too well-known as Superman and Geralt of Rivia, and I don't want to take him away from more Witcher series.

So for Harry Dresden, I'm going to go with Thomas Jane, who played a similar private-detective role (without the magic but with science fiction elements) on The Expanse.

Bob the Skull, Harry's sounding board at least at first, well, I'm going to go with Patton Oswalt because Oswalt is awesome. Probably limited to voice acting.

Karrin Murphy, a cop that eventually gets dragged into all the paranormal shit and becomes Harry's partner (in several senses of the word) -- well, I had to ask a friend about this, but Kristen Bell from The Good Place would be perfect.

Ebenezer McCoy is Dresden's mentor and (spoiler, sorry) grandfather, an old Scottish man. No, I'm not casting Sean Connery. I like Peter Capaldi, the 12th Doctor Who, for the role.

There are, like, a million other characters, as you'd expect for such a long series of novels. I mean, Mark Sheppard has to be in there somewhere because he's Mark Sheppard, but I don't know who he'd play.

In the end, though, I just want this to happen. I need this to happen. No matter who gets cast, as long as the series is as awesome as the books. Because polka will never die!

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