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:

Write_Mikey_Write!

about 6 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 8 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.

August 28, 2020 at 12:07am

#991729

Good? Evil? A Jedi Cares Not For These Things

Hey look, something relevant to fiction writers today.

https://aeon.co/essays/why-is-pop-culture-obsessed-with-battles-between-good-and...

The good guy/bad guy myth
Pop culture today is obsessed with the battle between good and evil. Traditional folktales never were. What changed?

Good guys don’t just fight for personal gain: they fight for what’s right – their values.

Personal gain is a value. Kind of a shitty one, but it's a value.

This moral physics underlies not just Star Wars, but also film series such as The Lord of the Rings (2001-3) and X-Men (2000-), as well as most Disney cartoons.

Couple of points: First, the X-Men comics may have been, at one point, good vs. evil, but the movies (absent the new one which hasn't come out yet) are pretty damn clear about the moral ambiguity on both sides. Professor X is the protagonist, Magneto is the antagonist (usually), but we see Xavier do some reprehensible things, and Magneto is shown to have solid motivation other than personal gain. Second, the Jedi are no angels; bending someone's will with the Jedi Mind Trick is the very definition of evil. And third, this article is from 2018; this year's X-Men title, New Mutants, is supposed to be the last film in that series -- which, of course, doesn't mean that Disney won't reboot it now that they have full rights.

That last one is beside the point; I just like superhero movies. This is the important part:

Virtually all our mass-culture narratives based on folklore have the same structure: good guys battle bad guys for the moral future of society. These tropes are all over our movies and comic books, in Narnia and at Hogwarts, and yet they don’t exist in any folktales, myths or ancient epics.

The rest of the (somewhat long) article basically expands on this.

In old folktales, no one fights for values. Individual stories might show the virtues of honesty or hospitality, but there’s no agreement among folktales about which actions are good or bad. When characters get their comeuppance for disobeying advice, for example, there is likely another similar story in which the protagonist survives only because he disobeys advice.

No wonder people are so confused all the time.

In the Three Little Pigs, neither pigs nor wolf deploy tactics that the other side wouldn’t stoop to. It’s just a question of who gets dinner first, not good versus evil.

I usually root for the wolf because bacon is delicious.

On a side note, I ventured into a movie theater the other day. With a severe lack of choice, I went to see Unhinged, the Russell Crowe thriller about road rage. I was the only one in the entire theater, incidentally (and yes, I followed all the guidelines for safety except for the one about "don't go to the movie theater.") I won't spoil it, but I made the mistake of reading the reviews first, so I went in expecting to be disappointed -- but it's actually not bad. Terrific acting, really impressive stunt work and car chases, and the plot hangs together pretty well. The reason I'm bringing this up is that it's relevant to this article: there's a good guy (er, girl) and a bad guy (Crowe, and please spare me the corvid-19 jokes), and on the surface at least, it's black and white. Thing is, and I think this might be why a lot of people don't like the movie, I thought his motivation was kinda flimsy, and her character was uninteresting to me. Perhaps they tried too hard to make it black and white, or, perhaps, they tried too hard with the motivation. After all, Jason doesn't need motivation to run around slashing teenagers, does he?

Anyway. No need to quote more from the article; if you're interested in this sort of thing, check it out. Like I said, it's kinda long, but I think it's a good essay on how storytelling has changed. And the conclusion -- the discussion of why it has changed -- is kinda chilling. Though not so much as the idea of a road rager who believes in disproportionate retribution.

4 Like • Comment • View 2 comments

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