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 9 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

October 11, 2018 at 12:47am

#943191

Here We Are Now. Entertain Us.

One bit of popular entertainment that I enjoy is film and TV adaptations of comic books.

This is a good thing, as there's a lot of that going on these days, from both of the classic publishers (now part of entertainment giants Warner and Disney) as well as a lot of independents. Sure, some are better than others, but that's true of every genre.

But, if you remember from a few days ago, I hate commercials. By which I mean, I really despise them with the all-consuming fire of a thousand pulsating Wolf-Rayet stars, and I will go out of my way to avoid them. This isn't a problem for many of the shows that I like, such as the Defenders tie-ins from Marvel, which are on Netflix and thus included in the cost of my subscription, ad-free.

I get around it for other shows, like the DC adaptations including Arrow, The Flash, and Legends of Tomorrow, because I bought the seasons from Amazon. See, as much as I hate ads, I don't pirate things. I haven't been published yet (and probably never will), but if I were, I'd be pissed if someone infringed on my creative output, so I don't do it. But I have no problem paying reasonable amounts for content that I enjoy. Therefore, I won't, for example, pay HBO just so I can watch Game of Thrones, but I do pay CBS so I can watch Star Trek and Salvation. Other people have other priorities, of course.

Make me pay for ads and I will cut you. (As I mentioned before, CBS does show some commercials even on the higher subscription tier, but they're short and not for consumer products and there's only one of them per episode so I'm putting up with it for now.)

Anyway, point is, the aforementioned DC adaptations (produced by The CW) have started up their new seasons again, and I was looking forward to doing what I usually do, which is buying them from Amazon. The episodes would arrive there the day after they aired, which was fine. But for some reason, they don't seem to be doing that this season. Pisses me off.

I tried, though. I tried watching The Flash on the CW's website. That at least had the advantage of being free, though with ads.

I couldn't get past the first group of interminable and intelligence-insulting commercials, and judging by the pips on the player, it looked like there were something like 8 clusters of ads I'd have to sit through to get content. All I can say about that is fuck that.

So I guess it's back to Netflix to watch old episodes of Supernatural (coincidentally also a CW production), which I had never seen before. It's not bad, but it's not my usual thing, and I was really looking forward to some cheesy superhero stuff.

But this proprietary streaming shit is getting out of hand. Even Disney and Apple are getting into the game, and soon probably everyone else as well, so by the time it's done we're back to the cable TV "channel" nonsense. I already know I'm not going to get a subscription to everything, so there will certainly be popular entertainment that I'll miss out on. Oh well. Nothing different there from a life spent without cable TV.

At least Doctor Who is still available through Amazon. For now.

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