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

1 Like

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 11, 2020 at 4:31am

#995608

If You Can't Stand the Heat...

We're already up to entry #5 (of 8) in

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts July 1!
#2213121 by Turkey DrumStik

Kitchen-Dick Road

"But Waltz... this is the third one you're doing a street name. I thought you said these things are random?" These things are random. That's why a bunch of them are clumped together. Sure, I use an app on my mobile which generates what's called a pseudo-random number, but it's statistically no different from rolling a hypothetical 16-sided die. The nature of randomness is...

...Oh, never mind. The reason I'm posting so late (for me) today is that after regaining consciousness from a thorough drunk pass-out, I got sucked into a YouTube rabbit hole of mathematical and physical oddities and, dare I say it: complexities. This led me to contemplate some of the deep mysteries of the universe, not in anyway related to roads, kitchens, or dicks.

Or are they?

After all, it doesn't take much to generate statistically random processes is one's kitchen. Happens all the time. Every day. Multiple times a day, for some people. Just boil water, and you'll see chaos in action, and chaos shares certain properties with randomness. Like... you know that water is going to eventually boil, but the exact location and size of the bubbles of steam? Unpredictable, within boundary conditions.

When I do road trips, I also use randomness. During my first cross-country road trip, as I'm sure I've noted before, I got it in my head to drive from the easternmost point in the continental US (in Maine) to the westernmost point (in Washington). Apart from these two boundary conditions, I had a few others:

Avoid interstates, stick to secondary roads.

No less than four and no more than eight hours of travel in a day

Stay within the US; a great-circle route between the endpoints would be over 90% in Canada

Select a random endpoint within a particular radius of a theoretical six-hour drive to stop for the night

This is not an exhaustive list, and there were some deviations from the plan, for example when a friend invited me for Thanksgiving dinner and their house was, well, close enough to the semi-random route. And when I nearly got buried in a snowstorm in Vermont

.

What I'm getting at, though, is that the last stage of this odyssey took me west of Seattle to the Olympic Peninsula of Washington State, and through a little town called Sequim, on the northern coast of the peninsula. And it is just outside of Sequim that the infamous Kitchen-Dick Road resides. So of the four road names in this blogging exercise, this is the only one that I can positively say I've seen - though I have no memory of seeing the sign itself, K-D Road intersects U.S. 101, and I'm certain that was the road I took because... well... look at a map of the area. There are no other through roads.

As for the name, the origin appears to be as mundane as it gets. There was a guy named Mr. Kitchen. There was another guy named Mr. Dick. The remarkably straight, north-south road between their farmsteads, or whatever they were at the time, was named after the dudes. Still, you have to think that whoever decided to name it that instead of, I dunno, Remarkably Straight Road or North-South Drive or Olympic View Boulevard, knew exactly what he was doing and was snickering like Beavis and/or Butt-Head the whole time.

How do I know this? Well, for once I could be arsed to look it up.

https://www.king5.com/article/life/style/best-nw-escapes/kitchen-dick-road-the-s...

Kitchen-Dick Road: The strangest street name in Washington

Okay, well, Washington's a big state, though admittedly with a low density of roads compared to, say, anywhere east of the Mississippi. But there have got to be other contenders for "strangest."

Additionally, according to that (very short) article at the above link, which also sports a very helpful photograph...

And it gets even better… The street actually intersects with Woodcock Road.

*cue more Beavis and Butt-Head chortling*

But the best part? The best part is something they conspicuously leave out of the article.

And there's a great reason for the name: two Sequim pioneer families, the Kitchens and the Dicks lived at either end of the road. They combined their names to name the road. This from Peggy Hardin Hunt, who's husband is the great grandson of William Dick, one of the pioneers.

Which could have made her name "Peggy Hardin Dick-Hunt."

*cue Beavis and Butt-Head dying of asphyxiation*

So next time you need a meetup location, considering telling your friend “I’ll meet you at the corner of Kitchen-Dick and Woodcock,” because it doesn’t get any better than that.

The chance of me ever setting foot on the Olympic peninsula again is perilously close to zero; Forks exists there. But you never know - an ex-girlfriend of mine, someone I still talk to occasionally, lives on nearby Whidbey Island. So it could happen. That would be pretty random, though.

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