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 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').

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.

June 2, 2022 at 12:01am

#1033199

Don't Do It

Here's my first entry for June's "Journalistic Intentions"

[18+], with a theme of tropes.

Ripped from the Headlines

For anyone too lazy to click on the link (as I usually am), to summarize: this is when a show or movie or whatever is based on current events. It's not usually a true story, but if, like, there's a story about some priest sexually abusing an altar boy, the movie will be about a different priest sexually abusing a different altar boy.

Not that anyone has the balls to actually make such a show.

I don't care about such shows. By which I mean, I don't give a shit if something is based on something out of real life, or entirely made up. Well. It's not like you can entirely make something up, or entirely be accurate to the details of a real event. Even the most outlandish science fiction or fantasy at least adheres to some anchor in reality, even if it's only to consider what one would do in a weird situation.

But there is one instance of this trope that I absolutely will not watch or read, and that is a COVID story.

Fortunately, I haven't seen anything like that yet. That doesn't mean it's not out there. It probably is. It's not like I'm aware of everything that gets released. But if I become aware of it, I'll wish I hadn't.

I don't want to see a movie based on the masking argument. I don't want to read a book centered around the vaccination argument. I really don't want to see anything titled "Love in the time of Coronavirus" or anything similar to that.

And above all, I will puke my fucking guts out if I even hear the merest whisper of a romance that involves two (or more; I'm cool like that) people managing to find a way to hook up in spite of social distancing and mask mandates.

No. I want my entertainment to, ideally, forget that the 'rona is or was ever a thing. I want my fiction to go on like nothing ever happened, like millions of people didn't die from it.

Just don't do it.

Failing that, at least don't make it central to the plot.

Pretty much any other current event is fair game: climate change, civil unrest, school shootings, war in Europe, terrorist incidents, whatever. I'm just not going to put up with covfefe-19 plots. Period. The only masks I want to see in movies or on TV are the ones worn by superheroes and the villains that oppose them.

And why? I know I should be able to, as a writer, articulate exactly why this is. The block, I think, isn't about writing, but more emotional -- a visceral reaction to overusing something that's occupied our brains enough for the past 28 months or so. Note that I'm not saying we should pretend, collectively, that it's not happening or didn't ever happen. Just that I don't want it encroaching into my fiction.

Other than that? Rip the hell out of the headlines. Truth can be stranger than fiction and all that. Just stay away from a certain virus.

You know. Avoid it like the plague.

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