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

September 7, 2022 at 12:01am

#1037430

Going Out

Why do I keep finding articles about the (shudder) outdoors?

10 Reasons People Get Lost in the Wild

1. Because they go into the wild
2. Because they go into the wild
...
10. Because they go into the wild.

Between the years of 1992 and 2007, our national parks were the site of 65,439 search and rescue (SAR) incidents.

Did they get billed? They should get billed.

From these thousands of SAR missions, a large percentage of “call outs” involved outdoor enthusiasts who had become lost in the wild.

...what were the others? Indoor enthusiasts who got lured into the forest, perhaps with the promise of hot nymph sex?

But with all of the technology we have today—such as cell phones, GPS devices, and satellite phones—how does this still happen?

The article specifies 1992-2007. Accurate personal GPS wasn't available until 2000, halfway through that time period. I'm curious if that made a difference, but not curious enough to be arsed to look it up.

So what kind of blunders leave people floundering and lost? Read on to discover the common pitfalls of wilderness navigation, and how to avoid them.

Not to pummel a deceased equine, but the easiest way to avoid them is to NOT GO OUTSIDE.

Misjudging Distances

With a heavily laden backpack, every mile you trudge may feel like two miles.

More like two thousand.

Unless you are skilled at pace counting (likely from military service, which we thank you for), the average person will have to make a wild guess about the distance they have traveled when “mile marker” features are absent.

I just count cross streets.

Once you have a handle on the amount of ground you normally cover in any given situation, you can use the amount of time to help you calculate your distance traveled.

Or you could—just spitballing here—carry a GPS unit (and a backup).

Inattention To Surroundings

At this point, the article features a helpful photograph of a rattlesnake. There's a story going around that rattlesnakes are evolving to lose their rattles due to selective extermination of the rattling ones. While it's nice that certain people are finally acknowledging that evolution by natural selection happens, in this particular case, there's no evidence for it.

In any case, nope ropes are but one of many reasons not to go outside.

Letting Egos Run Wild

We all know “that” guy. He’s arrogant, bombastic, and feels he can do no wrong. He’s also a statistic.

I don't know "that" guy. Wait, does that mean I'm that guy? No... no. Can't be. I know better than to go out into the non-indoor part of the world.

Traveling in Tricky Terrain

Flat and featureless landscapes with no distant landmarks can be trying to travel.

And are generally pointless to explore.

Map Mishaps

Don’t rely on digital devices alone for navigation.

This one, I actually agree with. Not with regards to venturing into the trackless wilderness, of course, but even just on a road trip. I always have 2 GPS devices and a paper map. Or at least I did when I had a car. I might get one soon; we'll see.

Following a Game Trail

More like "following a bear trail."

Getting Caught in the Dark

Okay. Yeah. This happened to me once. I've written about it before; no need to rehash my idiocy right now.

A Turn in the Weather

Some of my favorite schadenfreude-laden stories are of people going hiking on Mount Washington in New Hampshire, which basically has its own weather system disconnected from the rest of the troposphere. One time, the observatory on that mountain recorded a wind speed of 231 miles an hour.

That's enough to blow you off the mountain and into Canada.

Taking a “Shortcut”

To be fair, this is a Bad Idea in the city, too.

Splitting Up

There’s definitely strength in numbers. We all seem to know this instinctively. Yet, for a wide range of reasons, people will leave their hiking, camping or hunting group and become lost.

Anyone who's ever played D&D, or watched a horror movie, knows damn well that splitting up is always a Bad Idea. We have a saying: "Let's split up. We can cover more ground that way." Because we can individually cover more ground when we walk into an ambush and die, splattered all over said ground.

Now, don't misunderstand me—I love the wilderness. And I'll happily look at pictures of it.

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