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.

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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

August 11, 2024 at 9:14am

#1075049

Revisited: "It's a Trappist!"

Well, this entry from July of 2020 is embarrassing: "It's a Trappist!"

For starters, it wasn't the first time I'd used that title. In my defense, it's a truly awesome pun combined with a Star Wars reference joke, so I tend to use it a lot.

The entry itself was a response to a 30DBC prompt that went like: "If you won a free trip to any foreign country, all expenses paid in your own private jet and had the time to go (and there were no travel restrictions due to a global pandemic

), what is the first foreign country you would visit? Who would you bring with you? What would you spend your time doing?"

And I think we all know the answers to those questions as of 2024, but four years ago, things were a bit different.

Last year was my mostly-stay-at-home year. Not only did I want to conserve money for upcoming trips, but I wanted to lose weight so I wouldn't look like a typical American.

I was mostly successful at both.

I got even better at conserving money for upcoming trips because I could barely go anywhere for four years. The weight thing, I don't talk about.

The plan was to go to Scotland in May with a friend for the Islay festival.

That might still be my next venture. Obviously, it hasn't happened yet.

This shit will not be resolved by next year. So I doubt I'm going to Belgium or France. Or Scotland. Or the Netherlands. Or Belize. Or even travel in the US.

Oh, but I did end up doing a road trip in the US the following year. That did not end well (though it could have been a lot worse).

I'm prone to depression and this shit is not helping. Not the pandemic, not the travel restrictions caused by the pandemic, and certainly not prompts like this one. The only thing I have to look forward to these days is travel and death, and it looks like the latter is going to happen before the former.

See, this is why I'm a pessimist. Either I'm wrong, which makes me happy, or I'm right, which makes me happy. If I were an optimist, I could only be disappointed by the results.

Even if I somehow manage to stay alive and reasonably healthy (unlikely), my passport will probably expire before I get a chance to travel again. And I haven't even used it since I last renewed.

The major impetus behind planning a Europe trip this year is to use that damn passport before it expires.

But right now? In the utterly impossible scenario above? Belgium. With my friend, as I mentioned, and whoever else wants to go. Primarily, I'm interested in immersing myself, at least figuratively, in Belgian beer. Trappist ales, saisons, whatever. I can get some of them here -- I just had a nice couple of bottles of Delirium Nocturnum yesterday, and there's still one in my fridge along with a big bottle of Kwak -- but as with California and wine, they keep the really good stuff for themselves.

Coincidentally (or not), I have some Delirium Nocturnum in the fridge right now. It's very difficult to find Kwak here.

So the rest of that entry was just responding to the prompt. I'll be traveling alone, and also visiting France, so, not exactly what I had planned (which I don't mind), but dammit, at least it's (probably) going to happen and I can stop annoying everyone with "what I wanna do" posts.

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