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.

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.

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.

2 Like

November 17, 2020 at 12:01am

#998543

Past Perfect

I've actually had a perfect day. Several of them, in fact.

PROMPT November 17th

In your entry today, plan yourself the perfect day. Who would you see? Where would you go? What would you do? How do you spoil yourself?

Each of those days was different, but they all had three things in common: friends, booze, and food.

The food part shouldn't be surprising. Most people eat every day, anyway, and I would never call a day of fasting "perfect," regardless of anything else that happened on that day. But for me it's more than mere sustenance; it's a destination and experience in itself.

I'm sure the booze part isn't surprising if you know me. But I'm not talking about overindulgence; just something to add to the pleasure of the experience.

The "friends" part surprises even me, though, because I tend to be solitary. And yet having other people around to share the experience is a good thing; I just need some time alone afterward.

Location doesn't matter much, either. I've had excellent experiences close to home and on the road.

So let's look at what a perfect day for me might look like... assuming, of course, that a certain disease is no longer a concern. I should also point out that in this scenario, the temperature never dips below about 65F. I don't care how hot it gets, though, as long as the places we go have a/c.

Morning

First -- and this is absolutely critical for a perfect day -- I'm not woken by cats, people, weird noises, or, most importantly, an alarm. I just wake up when I'm ready. Hopefully this isn't too late for breakfast.

Breakfast itself could take one of several different forms. Cooking is work, so I'm at a restaurant or diner. They'll want to give me coffee; I'll request tea instead. They'll look all kinds of confused and thrown off stride. This is good; keeps them on their toes. Hopefully they'll have something besides that puke-orange Lipton bullshit. If not, I'll order a Coke. They'll try to pass of Pepsi as Coke. This is insupportable. Water it is, then.

Sigh. Okay, that's not a "perfect" day; that's just how breakfast usually goes for me on the road. Ideally they'll have an English Breakfast tea. Fortunately for me (and for servers everywhere) I'm not nearly as picky about my food as I am about beverages. Eggs Benedict, or a bagel with lox and cream cheese, or waffles, pancakes, toast, whatever, with some variety of eggs, and bacon. But really, any sort of breakfast food is fine.

The places I want to go don't open until 11 or so, usually, so I take my time with breakfast. That's when I'll meet up with my friends and we start drinking.

Not serious drinking, but visiting wineries, breweries, and/or distilleries and sampling small amounts of their wares. Wineries can be tough because they tend to be out in the country and you need to find someone who's not drinking to give you a ride. Some breweries are, too, but a lot of times they're in town and if you can't walk to all of them, there's rideshare. Even though I'm not drinking all that much, I'm not going to risk driving.

Afternoon

Lunch -- probably at one of the breweries; lots of them have decent menu selections. Then more samples of fine adult beverages, and maybe a walk in a park or a fun section of whatever town we're in. If we see something interesting, great, we can stop and check it out. I'm pretty flexible in that regard.

After all that hard work, I'll need a short nap.

Evening

No, I'm not cooking dinner, either. And I'm not too picky about where we eat: American, Italian, French, Japanese, Indian, whatever, as long as it's not lousy chain food. And the place, of course, has an appropriate selection of booze to go with the meal, preferably including expensive single-malt scotch that I can enjoy as a dessert. Even more ideally, they'll have some sort of music as well. Just not jazz. Fuck jazz.

And then, after dinner... dancing? No hell no. A movie? Nah, can see a movie anytime. A romantic walk on the beach? No squared to the power of nope. There's very little I hate more than having sand in my shoes, but one of those things is walking barefoot on the beach. And the only thing I hate worse than walking on the beach in the daytime is walking on the beach at night; I don't care what the scenery is like. So, what then? Well, more drinking of course, again somewhere that has decent music ("decent" still being defined as "anything other than jazz").

Night

Uninterrupted sleep.

Such a day could happen again, I think, though it may be a while. In the meantime, I'll just have to make do with hanging around with my cats, reading or watching movies, and writing.

There's still beer involved, anyway.

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