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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

December 2, 2020 at 12:05am

#999502

Frittered Away

I'm adding in some prompts from "JAFBG"

[XGC] for now, because December.

"30-Day Blogging Challenge ON HIATUS"

[13+]:
2. Today is National Fritters Day!
Write about your fave and if you haven't had fritters, would you like to try one?

"JAFBG"

[XGC]:
What is the most overrated holiday movie of all time? What should people watch instead?

Every holiday movie is overrated. Yes, even that one. That one, too. All of them.

Which doesn't mean they all suck, exactly, but way too much sentimentality is attached to all of them, beyond their worth as stories. They achieve an unwarranted mythological status; hence, the overrated bit.

But right now, and for the last oh, 40 years or so, I've considered the most overrated holiday movie to be Rudolph.

I ranted about that animated piece of drivel way back in 2007, and since then, I've seen these sentiments echoed elsewhere on the internet. I'm not saying people have copied off of me; I don't have that kind of reach. But it annoys me that something that I invented, this way of looking at a certain crimson-schnozzed reindeer, was popularized by someone else. I mean, it's like, way back in the 80s I invented a trick at fraternity parties where I'd hold two solo cups full of beer in each hand -- okay, it wasn't what I'd call beer these days, but I thought it was in my youth -- and let the sparkling amber contents fountain from cup to cup to cup to cup, eventually reaching my eager lips.

I mention the beer cascade thing because a few years back, I saw a picture of someone doing this with a caption like THIS MAN IS A GOD AMONG MEN and I got really pissed off because I INVENTED THE BEER CASCADE DAMMIT.

Pant. Pant. Pant. Deep breath. Okay, moving on. Where was I? Right, Rudolph.

Here's the original Rudolph Rant in all its glory, rated GC for dirty words:

The Rudolph Rant

(GC)
I ain't guiding no sleigh!
#1347370 by Robert Waltz

Now, I'm not entirely immune to feeling joy during the holiday season; it's just that everything about it, not just the movies, is overrated. But there are things I like about it too. One of them is a tradition I've had for the last, oh, must be nearly 15 years now, which was to go to a friend's house every December and attend their holiday party, which celebrates Hanukkah and Christmas. As a kid, I celebrated Hanukkah, and there was one part of that holiday I enjoyed above all else. Okay, above all else except all the presents. I'm talking, of course, about latkes. And my friend makes a mean latke.

It was easy at first, because they lived in the Northeast, a quick drive or train ride away. Then they upped and moved to California, which is a little harder for me to get to, but I managed. Every. Year.

Until... of course... this fucking year.

So it falls to me to make my own latkes for once. When I was a kid, we cheated and used store-bought latke mix because my mother, who was a wonderful person in many ways, was a ridiculously terrible cook. This year, I found a recipe that looks promising, although it also looks like a lot of work, and we all know how I feel about work. For latkes, though... it might just be worth it.

Right now a bunch of you have either already googled it, or are asking "wtf is a latke?" Well, I'm here to enlighten. Latkes are like fritters: vegetables shredded and mushed together and fried. Historically, whatever vegetables were available were used: carrots, parsnips, turnips, whatever. Jews in ghettos in Europe couldn't exactly be picky. Nowadays, the go-to vegetable for latkes is the potato, which, well, to be fair, didn't exist in Europe for a long time, but once it did, boy did Europeans take over that shit.

Anyway, basically you shred the potatoes, mix in some onions and seasonings, and fry those suckers up in a quarter-inch of oil. The oil is important, see, because it symbolizes the oil in the lamp in the temple where the Hanukkah miracle happened. (Everything symbolizes something. Metaphors are fun!) But it's also important because it's not a latke unless it's fried. None of this healthy vegan namby-pamby air-fry bullshit. FRIED. IN OIL. ONLY.

Lots of cultures have similar things, like pakora in India for example, one of my favorite fried foods. Hell, Japanese tempura can be considered in the same class or family of culinary creations.

I mean, really, who hasn't had fritters of one sort or another? Unfortunately, I won't have the ingredients for any of them today, so I can't celebrate National Fritters Day as the gods intended. I guess I'll just have to watch a movie instead, though not a holiday one. Yeah, yeah, I know, latkes aren't technically fritters. So what? I say they count, and I INVENTED THE BEER CASCADE. If you're not careful I will explain exactly why a hot dog isn't a sandwich.

Oh, and the one holiday movie that's less overrated than all the others?

Die Hard, of course.

Yippie-ki-yay.

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