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 14 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 16 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.

April 23, 2022 at 12:04am

#1031212

Swamp Life

I want to talk about this article, but I don't want to get too bogged down.

The Hidden and Eternal Spirit of the Great Dismal Swamp
For nearly all of its modern existence, the Great Dismal Swamp has been excluded from U.S. history. Now there’s a push to bring its significance to light—and it’s revealing what really goes into remembering the truths of our ancestors.

This swamp is in my state (and also extends into North Carolina), and I've been there. It may not be as famous as the Everglades, but it's pretty cool in its own way. For one thing, it contains one of only two lakes in Virginia that were not formed by human-built dams.

That said, the article's author apparently subscribes to the New Yorker school of rambling prose. It irritates me. For example, the lede:

By a quarter past eight, the woods were bright and humming, and the summer heat had rolled in off Route 17. The early August air was soft and humid by the canal on the eastern side of the Great Dismal Swamp’s Virginia half. The bikers, the joggers, the hikers, the bird-watchers, and the couple loading up their dusty SUV each chimed “morning” one after another, all cradling the letter m at the roofs of their mouths.

Honestly, normally I'd Stop Reading Right There. Too many linking verbs, and that last sentence is just so fucking precious. But as I said, the subject matter interests me. I've been to the Great Dismal, even hiked a ways into it.

The article starts out with some of its history, especially as it relates to slavery when there was still slavery there. Then...

Since the beginning of the 20th century, protection of the Dismal has been framed as an environmental issue. After 200 years of heavy logging left the territory at less than a third of its original size, the Union Camp Corporation gifted the swamp to the U.S. government in 1973.

And honestly, it is an environmental issue. For a long time, swampland was considered a nuisance, something to be "drained" or "filled" or "reclaimed." But of course swamps (honestly, I'm a bit vague on the differences between swamps, marshes, bogs, etc., so I'm using "swamp" generically) are wetlands, and hopefully I don't need to explain just how vital wetlands are in ecology.

All of which is interesting enough, but I already knew that. What this article does is delve into the human history of the place. It's long, but again, I think this is stuff that needs to be more in our consciousness.

And be warned: some of it is quite graphic.

Still, some of the photography is very striking.

6 Like • Comment • View 1 comment

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