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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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.

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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.

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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.

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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.

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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.

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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

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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.

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February 18, 2021 at 12:04am

#1004723

The House of the Spirits

Entry #5 of 8 for "Journalistic Intentions"

[18+]

The House of the Spirits

I'm going to start this entry by saying that I've never read this book; I've never heard of this book; and I have not a single clue what the book is about. I mean, really, it could be almost anything:

A person with more than one personality

A haunted house

A church or other religious building

A columbarium

Seriously, just consider all of the various possible meanings and/or connotations of "house" and "spirits" and you're good to go.

Incidentally, because of that last bullet point, this is cheating on the part of whatever author wrote it (like I said, I haven't the faintest clue about the book in question and I'm deliberately not looking it up before doing this entry). It's cheating, because when you have words with that many definitions and connotations, you can employ a great deal of parallelism, and people respond to symbolic parallelism.

And so I'm going to talk about my favorite thing that could be considered The House of the Spirits:

A bar.

I miss bars. I miss them a great deal. Oh, sure, I've gotten more into mixing my own drinks -- everyone needs a pandemic hobby -- but there was something about sitting at a bar and having a lot of options to choose from, and not having to mix them myself.

I will say this, though: one drink I made called for mint leaves. I tried to get mint leaves from the supermarket, but they were out. Instead, I opted for a mint plant, an actual living potted thing with stems and leaves.

Plants never last long around me. They usually take one look at me, say "Oh hell no," and commit suicide. This one has somehow stuck around for... I don't know... two weeks? Something like that. Time has little meaning anymore. More than a week. Less than a month. I mean, it was kind of iffy there for a while, and my housemate helped, but somehow this plant still lives; I've been pruning it occasionally for leaves, and there's even new growth starting.

But see, if I could go to a bar, I could just order a drink and the mint leaves are already cut and the bartender does all the actual work. And I wouldn't be limited to just the 25 bottles I have on hand.

The drink in question, by the way, is called a Ginger Rogers

and I mostly just started making them because I had a metric ton of ginger to use up and I like gin a lot. Yes, the name is a pun because of course it is.

But since I had to also buy the mint plant, now I'm almost out of ginger and have plenty of mint, so soon I'll have to buy more ginger (and gin) in order to use the mint because I can't just let the plant grow out of control. This happens a lot. Say you want ham and cheese sandwiches. So you buy ham, cheese, bread, lettuce, tomatoes, whatever. You run out of ham, so you buy more. But then you run out of bread and you can't let the ham and cheese and veggies go to waste so you buy more bread. Then the cheese runs out and you can't have a ham and cheese sandwich without cheese, so you buy more cheese. Meanwhile, the remaining veggies have gone bad because it's been two days, so you have to buy fresh ones of those and while, sure, you can probably just make a salad you still have ham, cheese and bread so you make sandwiches but then the ham runs out again and you buy more ham... the cycle never, ever ends.

And that's another reason I prefer to go to bars and restaurants.

It's been my tradition for a while now, on my birthday, to drink tequila. Lately this has happened at one or another local tequila bar. Not this year. But I'm prepared. I have a bottle of tequila, a bottle of triple sec, some limes, salt. But I'll probably run out of one or another of those things and have to replace it, and then run out of another and have to replace that. Until my spirit gives up the ghost. The ham and cheese sandwich effect, you know.

So since it's my birthday, it's time for me to give someone a present...

Merit Badge Mini-Contest!

Give me a mixed drink recipe. Link it or type it in, I don't care. And I don't want to leave out my non-drinking readers, so I'm not saying there has to be alcohol involved, just make it an interesting mixed drink (e.g. no "virgin screwdriver," which as far as I know is just orange juice). Out of all qualifying comments, I'll pick one commenter at random to give them a Merit Badge tomorrow. Deadline, as usual, is midnight tonight, Thursday, WDC time.

And if I like a recipe I might even try it out sometime.

One thing, though: I usually post just after midnight because it suits my schedule. This will probably not happen tomorrow because, well, see above about "tequila on my birthday." I will post and choose a MB recipient sometime later on Friday, though, if the tequila doesn't kill me.

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