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').

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

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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

December 3, 2020 at 12:01am

#999558

Stuff and Nonsense

For the record, I'm selecting JAFBG prompts using a random number generator, for maximum chaos.

"30-Day Blogging Challenge ON HIATUS" [13+]:
3. National Roof Over Your Head Day!
Tell us about the favorite room in your home.

"JAFBG" [XGC]:
What do you absolutely NOT want for the holidays this year?

I don't have a favorite room in my home.

What I do have is a home. That is, a relatively modest house in a quiet neighborhood that got picked for me by my first wife and her erstwhile business partner. They fell out, we fell out, somehow I kept the house. I decided I liked the house and its location, and so here I've been, absent a few months' worth of travel, for a bit over 25 years.

The last time I refinanced the house, it was on a 15 year mortgage that I managed to pay off early, so it's mine. All mine. MUAHAHAHAHA. No bank, no neighborhood association, just perfectly reasonable city regulations about grass height, snow clearing, not hosting crack parties, and the like.

I don't even have names for all the rooms. I mean, there's the kitchen, the bathrooms, and the bedrooms, one of which is oddly placed downstairs off the utility room that houses the HVAC, water heater , laundry facilities, and a whole lot of stuff. My housemate lives in that bedroom. I mostly keep to the upstairs area.

Also downstairs is a big room that I suppose would be described as a "rec room," because right now it's a wreck. In earlier times, it's been a lounge, a home theater (I still haven't replaced the projector, or the water-damaged sheetrock to which it was once attached), my computer area, a meditation place, and a gaming space, but right now it's kind of everything and I don't use it much. The rec room is covered with stuff right now, mostly belonging to my housemate, including her two guinea pigs who are very cute but kind of a mess. Right off of that is the downstairs bathroom, and it also has a door to the patio. The patio has collected stuff, but only waterproof stuff because the deck above it is porous.

Upstairs is more bedrooms, one of which is mine; the other two are a guest bedroom and my office. All three are chock-full of stuff. There's a bathroom, a kitchen, and a space off the kitchen which I suspect was intended as a living room but now contains a really nice, sturdy dining table, which I mostly just use to sit my laptop on because the office is full of stuff. The bathroom, oddly, doesn't contain much stuff, except the cabinet could use some organizing.

The kitchen has a door that opens up onto the aforementioned deck, which is badly in need of replacement before it collapses, but I've contracted with a guy to do that. Supposedly he'll get to it next year. The replacement won't be porous, so the patio might actually be mostly dry when it rains. The deck has a bunch of stuff on it. The kitchen has a bunch of stuff in it. The dining room is lined with bookshelves containing stuff.

You try living in a place for a quarter of a century, with a changing cast of other characters, and not collect stuff. I don't know; maybe you could do it. I certainly can't. I've been taking some time every day to deal with the stuff, but it's a Sisyphean task. Hell, I don't even know how to dispose of a lot of the stuff.

So I should buy a bigger house, right?

Okay, no. Then I'd have to move all the stuff. Besides, like I said, I like it here; it's in stumbling distance of at least five drinking establishments, depending on what you consider stumbling distance.

And like I said, I don't have a favorite room. Obviously I spend a third of the day in my bedroom, but I don't remember most of that time. The rest of the time I spend sitting on my deck with the laptop if the weather doesn't suck too badly, and that's not a room with a roof over my head, just a patio umbrella. When it's raining too hard, snowing, windy, or cold, I'll sit at the dining room table.

But hey, I'm just glad to own my own home. Which leads me to the other prompt (you knew I had to get to it eventually). My knee-jerk response to "What do you absolutely NOT want for the holidays this year?" is of course Trump Mumps, but that's way too obvious. The actual answer is "anything" because... dammit...

I have enough stuff.

But, you know, there's always room on my new Kindle... and there is that distressingly empty spot in my liquor cabinet...

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