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 12, 2020 at 12:04am

#995688

From the Ashes

Entry #6 for

Journalistic Intentions

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

politicalwatch@appliancerepairscottsdaleaz.com

I haven't been to Scottsdale, but I've been pretty close.

On one of my excursions, I decided to follow U.S. Route 60 from beginning to end. Or... I suppose it was end to beginning, considering that the US mostly developed east to west, and I was traveling back east.

Route 60 ends just east of the California border, because apparently, a while back, in a transparent attempt to begin its process of secession from the US, it took over the old US routes that ran across it, giving them new designations.

It's not as well-known as the storied Route 66, but I figured, hey, I'm in Vegas and I want to get back to Virginia, and the other end of the old route is in Virginia Beach. So I drove south from Vegas until I reached the end point of U.S. 60 and began the long trek home.

I don't live in Virginia Beach, of course, so this route would take me past my town (missing it by about 35 miles), but I'd long been wanting to trace one of the older, pre-interstate US routes from beginning to end. I have a friend who, until earlier that year, lived on a farm adjacent to Route 60 in Virginia, but that, and Pacific Avenue in Virginia Beach, had been my only experience with that road that I remember.

It's worth mentioning that yes, I'm fully aware that interstates get you where you want to go much faster and with more services available. But I don't travel for the destination; I travel for the experience of traveling.

Still, US 60 through Phoenix was one of the most stressful experiences of my driving career - and I've driven in New York, Boston, DC, LA, Atlanta, and the SF Bay area, just to name a few traffic-heavy places.

Phoenix. Sucked.

A few months after this trip, I saw a news story about a high-speed chase that the cops were involved in through Phoenix. My comment was I didn't believe it, because the top speed you can make through that shithole is, in my experience, approximately half walking speed. Okay, probably it's not a shithole, because clearly people want to live there. But the traffic sucks.

Anyway, the reason I bring this up is that Scottsdale is essentially part of Phoenix. Oh, sure, it has its own separate designation, but my rule is that unless cities are divided by a major river, a significant park, farmland, or a big honkin' wall or something, stop calling them different cities. It's annoying and confusing to anyone who doesn't live there, and I say that as someone who lives in the only state where cities are separate political entities from their surrounding counties.

But U.S. 60 doesn't go through Scottsdale, instead bypassing it to the south. Though "bypassing" doesn't convey the right flavor of traffic jam. After slogging through Phoenix, it was getting dark (I'm pretty sure I entered it in the morning), so I pulled off to spend the night at a motel in Mesa, which is another annoyingly city-that's-not-a-separate-city, directly south of Scottsdale. Or I don't know, maybe it was Tempe. Look, I've only been to Phoenix once and the chance of me being there again is minuscule. Okay, no, maybe it's not; I didn't have time to visit any breweries there, so it's still on my list. I'll just have to remember to allow a few extra weeks to get around the city.

From what I can gather, Scottsdale is, like, the rich people part of Greater Phoenix, so I wouldn't be allowed across the border anyway.

Which does nothing to explain or even hint at an explanation for the actual prompt, so my headcanon is that the appliance repair company is a front for a right-wing conservative pedophile, undocumented immigrant, human trafficking, and opioid distribution ring (hey, they're not the only ones who can make shit up), and that particular email address is for someone who follows the ebb and flow of politics so they'll have some warning when the government decides to start rounding them up.

Though they won't, because the government is in on it.

Following an old US route can get tricky at times, especially when it goes through a city and signs are missing or unclear. I must have looped around Louisville, for example, three times making sure I stayed on track.

And then, when I finally rolled into Virginia Beach a few days later, I stopped for the night just a few blocks short of the other end of Route 60, because that's where my favorite bar in the entire world is located.

Well. Was located. It closed last year, and I'm still sore about it. Add Virginia Beach to the list of cities I have no further reason to return to.

Unless a new brewery opens there, of course.

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