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:

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').

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

November 25, 2018 at 1:19am

#946241

Challenges

As some of you know, my entries this month have been based on prompts in "30-Day Blogging Challenge ON HIATUS"

[13+].

I figured if I'm going to try to write here every day anyway, I might as well go outside my comfort zone a bit and attempt entries based on other peoples' ideas.

When I was a kid, one of the writing exercises I did was to open a book to a semi-random page, grab a phrase or sentence, and expand upon it. This isn't really much different. Sometimes it's easy, and the words just flow. Other times, I have to think about it a bit. The challenge for me is to do something to make it my own - usually by means of comedy.

For a while over the past few years, the only thing I was writing were newsletter editorials, usually 2 per month. I felt like they were using up my entire creative urge, and some months I struggled to find topics. But, as I noted several entries ago, I found it doesn't really work that way, not for me, at any rate. The more I write, the more ideas I get. The more ideas I get, the more I want to write.

I guess the advice you hear is worthwhile: a writer writes. Maybe it doesn't matter that not everything is profoundly deep or funny, as long as you're writing. I should have known, really; I used to be a photographer back in the days before that medium went all-digital, and my trick was always to shoot half a dozen rolls of film in hopes of getting just one good image. And I found, then, that the more I shot, the more frequent the good images became. So yeah, if I'd been thinking straight, I might have concluded that something similar would apply to writing.

Thinking straight isn't always my strong point. But writing helps with that, too.

The hardest part of this challenge, for me, has been to write about things I wouldn't normally give half a shit about. But at least I've found that I can still write about them. This is important, because while it's good to concentrate on the things you care about, it's also good to branch out and learn new things.

If I had it all to do over again, though, the only thing I'd change is throwing in more comedy. Maybe a brick joke, but brick jokes are more funny to the writer than to the reader (a brick joke is the metaphorical equivalent of throwing a brick up in the air at the beginning of a story, and then, at the end of the story, after everyone's quite forgotten about the brick, it conks someone on the head). Or more repeated themes; what could be funnier than if I somehow worked a duck into every entry? Ducks are inherently funny, silly waddling quacking dinosaurs that they are.

Anyway, I've got less than a week left of this, and then it's probably back to (mostly) riffing on crap I find on the internet. I've got a backlog, now. I keep getting targeted with breezy articles about how to increase one's productivity. For some reason, the algorithms-that-be have me pegged as someone who gives a damn about that sort of thing. Spoiler: I'm not. But I have yet to see an article about how to reduce one's productivity, which would be more my speed.

Guess I'll have to write one.

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