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 2 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 4 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.

January 7, 2023 at 6:12am

#1042770

Yeast River

Still waiting for that other shoe to drop. It's going to happen. It's inevitable, because it didn't hit the ground yesterday.

I had some time to myself yesterday, so the gravitational pull of breweries was irresistible. There's a cluster of them in Queens, just across the river, and I felt them tugging at me all the way from Central Park. As it was too cold to swim (and I wouldn't swim in the East River on a good day for any amount of money—well, maybe a billion dollars, but no less), and subways didn't go quite where I wanted, I summoned an Uber.

Uber's very convenient and all, but I have no doubt that they, like every other bastard company in the world right now, is sucking up every bit of data they can find on you. This isn't normally a big deal, but most of my Uber rides either begin or end at breweries, and I'm sure that's part of their dossier on me. So while I was sitting there in the back of the car (the rideshare drivers in NYC have started installing bulletproof plastic shields just like the taxi drivers did years ago), I took the opportunity to check the weather online... and got treated to an ad for beer. Well, not really beer, but that mass-produced swill you find everywhere, but still, it's direct competition with actual beer.

This was almost as uncanny as the other day, whilst sitting in the doctor's office waiting for the goddamn slow as shit doctor, I went to play a game on my phone (there were signs up urging us not to use phones in the office, but fuck you; you make me wait one minute past the scheduled appointment, and my distraction comes out), and what ad did they push at me? Blood pressure medication. That was even more eerie because at the time there was a sphygmomanometer staring me right in the face.

Look, if I have to put up with ads anyway, which it seems that I do because we're in the end stage of capitalism and everything is a goddamned ad, I'd rather they be targeted than not. Obviously, I'd prefer to never see another ad. What's the point of having all my privilege if I can't use it to avoid getting bombarded by beggars? But failing that, it's better for me to see ads for fermented and/or distilled beverages than for, say, camping supplies.

Anyway. I did figure out one way around the Uber destination/pickup thing a while back, and it's especially useful in cities: instead of putting in your actual destination if it's a bar, brewery, or bordello, you use Google to find a more puritan-friendly business nearby. Like, I dunno, a nail salon or lawyer's office or bookstore. You have the driver drop you or pick you up there instead. Of course, this often means walking half a block, which I know is a tall order for some, but it might be worth it just to randomize their algorithm on you.

The downside of that is, naturally, that then you'll start getting targeted ads for nail polish or personal injury attorneys or the latest garbage NYT fake "bestseller."

Might be worth it, though, just to mess with them.

I didn't do that trick yesterday. Maybe later today.

Oh, as for the breweries? I visited four of them, and they were all decent.

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