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 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').

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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.

May 18, 2021 at 12:20am

#1010351

Screening

30DBC prompt is running late, will edit later, etc.

So yesterday, I got to perusing my local drafthouse cinema's movie offerings. As I've mentioned before, I've been back to regular visits to the movie theater. I saw Godzilla vs. Kong twice, the second time as a celebration of my friend's vaccine freedom (I'd achieved freedom two weeks earlier). In between, I saw Nobody, which was a great fun movie, in whatever genre John Wick is. Middle-aged white guy revenge fantasy, I guess. Like I said, a lot of fun. And on Thursday I'm going to go see Wrath of Man, which, well, all I need to know about it is it's a Guy Ritchie movie with Jason Statham.

Anyway, my questionable taste in film aside, like I said, I was looking at their upcoming calendar and I noticed something cool. Now, Alamo only posts a week in advance for new releases and blockbusters, but usually like two weeks out for older movies. So their weekend lineup for Memorial Day isn't complete yet.

But just about every single showing currently listed for that weekend is already sold out.

This doesn't affect me much, because I prefer to do my theater-going on weekdays. It's quieter and the people are more interested in the movies and less in just being anywhere that's not home. So I have no real desire to visit the cinema on any weekend, especially a holiday weekend in the US. (This does not mean that I never will.) But as far as I can tell, what this means is:

Movies are back, baby.

Now, look, I get it, some people prefer to watch movies at home. I'm not dissing that. I do it myself. And if this were just a standard theater with an overpriced popcorn and Coke concession, I'd avoid it too. But like I said, the theater is also a drafthouse with 32 beers on tap, numerous other drink options, and a varied food menu including full dinner (or lunch) options. And seat table service. Most importantly, any assholes who play with their stupid phones during the movies are thrown out on their ears.

Sure, I could stay at home, drink the booze I have here, fire up the internet, and whip up some tacos or something, but I like the movie-theater experience, with the big screen and the Dolby surround sound -- things that I could approximate here, but never duplicate. Yeah, it gets expensive sometimes. I'm okay with that. There are few things I'd rather spend my money on. I could say I'm just glad to do it after a year of enforced separation, but if you've been following along, you know I wasn't entirely absent from the cinema during that time. Closings and health-related restrictions interrupted my goal of seeing at least one movie a week there, though, and all I'm doing is getting back into that schedule.

Hell, I might even start doing quickie reviews of movies, here. I think I could make them entertaining, especially since I tend to see them drunk. I mean, why not? The theater's well within stumbling distance.

Edit:

PROMPT May 18th

What is the most ridiculous or one-of-a-kind thing you’ve ever bought? Tell us the story!

Yeah, I dunno... Drunk Me sometimes buys me presents, but so far they haven't been too ridiculous, and certainly not unique, being from Amazon. Even Drunk Me knows better than to go on eBay or Craigslist. And they're not as disgusting as the presents my cats bring me.

But I suppose my first car qualifies.

I mean, technically it wasn't my first vehicle, but remember: country kid here. I drove a pickup truck.

When it died, though, it was at about the worst possible time for me financially.

Now, look, I'm not a huge motorhead. But there's something I enjoyed about vehicles made before, I dunno, about 1995 or so, ones that you could mostly fix yourself with a few tools and not have to deal with computer diagnostics or warranty-voiding. And like I said, I was close to broke, and the truck was beyond fixing by anything short of replacing everything under the hood -- at which point you might as well get a new ride.

So I went to a used car auction and bought a complete POS that had a working engine and inflated tires, and that's all I knew about it. It cost me $300 plus the auction fee, or what would be the equivalent of about $600 now. It was a 1982 Corolla that had lots of issues, but passed state inspection -- barely. Best of all, being built in the early 80s, I could do a lot of the fixin' myself.

A lot of it, but not all of it. The biggest non-cosmetic problem with that car was that it was only firing on 3 out of 4 cylinders - much like my brain when it decided to buy the car. Honestly, though, this didn't affect it much, a testament to the engineering at Toyota at the time. I mean, it wouldn't go past 60 (that's 100 for y'all furriners) without screaming in terror, but I mostly needed it for city driving anyway. And the acceleration was predictably shit, but whatever; it ran, the brakes worked, and it didn't guzzle gas.

But that's not the most ridiculous thing about it.

No, the Ridiculous Award goes to me back then for what I did right after I bought it using the last of my cash and a few bucks I'd borrowed from a friend.

I puttered that thing from the auction block across the street to Crutchfield, where I had them install a $900 sound system, complete with subwoofer, on credit.

That's right. I put a $900 sound system into a $300 auction beater.

At least I had my priorities straight, right?

6 Like • Comment • View 6 comments

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