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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Write_Mikey_Write!

about 6 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 8 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

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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.

July 6, 2021 at 12:04am

#1013144

Shit Happens

So... I hit a deer.

Let me just start by affirming that I was in no way injured, so people who like me can be relieved and everyone else can hope for a more desirable outcome next time.

Still, I consider myself lucky. And because I don't have much else to do right now, as I'm in a small town in South Dakota, let me explain why.

First of all: preparation.

As I've noted before, I'm a pessimist. This means that I can only rarely be disappointed. Expecting that bad shit will happen can keep you from freaking out when bad shit happens.

In terms of my mental list of Things That Could Go Wrong on a Road Trip, "Collision" is up there near the top, with the subcategory "With Bambi" similarly prominent. ("Alien Abduction" is way down near the bottom, but I can't rule it out entirely.)

Before I left, I made sure I had current insurance and roadside assistance coverage.

I tend to drive at (or maybe just a bit above) the speed limit and wear my seat belt.

I shouldn't have to say this, but just in case: No, I hadn't been drinking.

Second, circumstances.

While the above can be considered making my own luck, obviously there's no way to predict when an accident will occur or how bad it will be. That's why they call it an accident. But still, circumstances worked in my favor to a remarkable degree:

It happened less than two miles from an upcoming gas station. This is kind of amazing, since in that part of South Dakota, on non-interstates, you can go 50-60 miles without seeing a town, let alone a gas station.

I wasn't knocked off the road and was able to keep going to said gas station, though the car surely wouldn't have made it much further with its front end damage.

The air bag didn't deploy. They tell me that a couple of inches to the right and it probably would have.

Though yesterday was a national holiday (for y'all from other countries, when a major holiday like Independence Day falls on a Sunday, they declare the following Monday to be the actual don't-work day), the station was open.

The gas station had an auto mechanic, and they too were open. (Stations with mechanics are a dying breed, even in South Dakota.)

While they couldn't do anything for the car, they took me to a "nearby" (by SD standards) town that maybe could.

That shop was also staffed on a holiday. (Though not with people who could look at the car; still, they were able to arrange that for the next day.)

There was a rent-a-car nearby, and they were able to shuttle me there.

It, too, was open and staffed.

There are hotels near the rent-a-car, and they had vacancies.

The rent-a-car is at a small regional airport.

That last bit is important, because my car is 11 years old so will probably be declared a total loss, which kind of leads me back to the "preparation" part -- I always figured in an emergency, I'd arrange for a flight home.

Now, yes, I'm a bit sad about the car; it's been a good car. At the same time, it was coming up on a major expensive scheduled maintenance, and I'd been toying with the idea of buying a different one anyway. And I'm also disappointed that I won't get to see my friend in Salt Lake City or anyone else on this trip -- but there will be other trips. Shit, you don't think a little thing like totaling my car is going to stop me, do you?

Well, sure, temporarily, yes, but you know what I mean.

Oh, and I looked at prices for flights home, and even with baggage fees it's still a lot less than I was about to spend in Salt Lake City on food and lodging.

Anyway, don't feel sorry for me; like I said, I always knew this was a possibility, and I know the risks of driving (they're much higher than the risks of air travel, for example). No, save your sympathy for the poor deer. I feel really bad about her, and I really hope she didn't suffer long.

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