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

October 31, 2020 at 4:04am

#997229

More Tricks Than Treats

I can't be arsed to riff off a link today. For the first time since March, I'm away from home and staying in a way-too-expensive hotel from whose window I can see a sliver of the Potomac. Also, the vending machine doesn't work.

At least the restaurant was good and had patio heaters for outdoor seating. They had scotch. Yes, I'm just now waking up from passing out from drinking almost enough scotch.

While I'm complaining about lodging (which, really, I shouldn't be, because I should just feel lucky that I finally get a small change of scenery, but in my condition I just want to complain about everything, including the fact that I continue to see today's full moon referred to as a "Blue Moon," which is WRONG), can I just say that if I spend the money to stay at something just a bit fancier than a Super 8, could they possibly put goddamned tea in the room? I don't even need the fancy artisan stuff. Hell, right now I'd settle for shitty-ass Lipton. Not everyone is a coffee drinker, but coffee drinkers get free coffee, and what do I get? I get having to put on my pants and a mask, trudge down to the lobby (because the vending machine is broken) and buy a way-too-expensive Coke Zero to get my needed caffeine to offset my incipient hangover.

Fortunately, I had the presence of mind to remember to bring my room key. One loses one's travel habits after seven months of moping about at home.

Later this morning comes the whole purpose of my travel, which is an hour and a half walking tour of Alexandria with a focus on the city's history of brewing. You'd never know it these days, though, since right now the nearest brewery is four miles away, and while it's big enough that I've had their beers before, I'd never visited Port City Brewing Company. Apparently, at Port City, they reserve the patio heaters for groups, and us lone wanderers have to huddle alone in the frigid shade. Worse, they're not even doing tasting flights, and you have to use a crappy smartphone app to order. How am I supposed to enjoy their full range of beers if I have to order them one at a time and not ask the bartender about them?

Anyway, I'm going to try to get a bit more sleep, but I didn't want to break my blogging streak, so here it is. And here's a link for you to laugh at: https://www.thedailymash.co.uk/news/food/people-who-pronounce-it-pan-au-shock-oh...

6 Like • Comment • View 4 comments

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