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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Turkey DrumStik

about 3 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!

a day 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

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').

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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

January 12, 2019 at 12:46am

#949466

Talent

Besides the craft of writing, are you an artist in any other medium? Sculptor, singer, dancer, painter? Share a story about your talent!

I have no talent.

This is a difficult thing for me to admit. In a society that values talent and good looks above all else, it makes me a pariah on both counts.

Don't think I haven't tried. Oh, I have a bit of skill at technical drawing; I started out as a drafter before I became a professional engineer. That's less talent and more attention to detail, though. It takes knowledge of geometry and an understanding of math, both of which I'm fair at, but there's little creativity involved.

I've also been a photographer, and even gotten paid for it. But I was never any kind of Ansel Adams; I merely applied my technical skills to things like composition and lighting. There, too, true creativity eluded me.

One thing I wish I had real talent for was music. I've studied music theory. I played piano, violin, and guitar. But I've always envied those who didn't have to read music, who instead could just hear something and recreate it on an instrument. It is fortunate for others that I'm something of a loner, because I do sing - though not well. Get me drunk at a karaoke bar and it's a different story, but I won't do that in my hometown. Otherwise, my love for music has to be limited to passive listening.

I do okay at cooking, but there was never any danger of me becoming a professional chef.

Okay, I do have one talent, but it's an utterly useless one: you know how you're always told not to mix different types of booze? Well, my talent is being able to completely ignore that advice. Fermented or distilled, any order, all day long. Sure, I get hangovers like anyone, but they don't seem to have anything to do with what I drink before or after other drinks.

I told you it was useless.

So, since this is related to my one ridiculous talent, I'll share a story.

One time, oh, must have been early 2017, I was sitting in my safe space (a bar) when I saw, on the wall, a bottle of Rumchata

. Rumchata is, as its name suggests, a rum drink, but it's important for this particular story to note that it's actually produced in Wisconsin. I'd been introduced to it on St. Thomas, where some friends and I spent half a day trying out different combinations of various rums and rum drinks, including Rumchata.

Now, I'd recently watched The Big Lebowski for something like the 147th time, and I'd been thinking of ordering a White Russian because I'm a Dudist at heart (except I really like The Eagles, man). But seeing that bottle of Rumchata gave me an idea.

"What if," I said to the bartender, "you made me a White Russian, but used Rumchata instead of cream?"

"Oooh," she said, either impressed by my drink-making creativity or, more likely, sensing a big tip in her future. "I can do that."

A White Russian (or as The Dude calls it, a Caucasian) involves cream (or milk), kahlua, and vodka. This particular bartender, whose name was Christy, substituted Rumchata for half the cream. That's okay; I figure her job is to make 'em and my job is to drink 'em.

I'm sure I'm not the first person to come up with that particular drink - I never am - but I'd never heard of it being done. When she was finished with her artistry, I declared it to be delicious.

"Now," I said, "we just need to name the drink."

"Oh, I don't know," she said, "I'd have to think about it."

"Well," I mused, after thinking it over, "Rumchata is a very American creation. But the vodka gives it that Russian influence. So I think we should call it... an American Election."

"Oh, that's just wrong."

So that's how I invented a drink that had probably already been invented, but gave it a name that's purely Waltz.

7 Like • Comment • View 9 comments

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