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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 8 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 10 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.

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.

July 14, 2020 at 12:17am

#988106

It's a Trappist!

Godsdammit.

PROMPT July 14th

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?

Now? I'm going to do this prompt NOW?

I've said some of this shit before, but I'm going to say it again for any new readers, and because I'm fucking pissed. In the American sense, not the British.

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.

The plan was to go to Scotland in May with a friend for the Islay festival. One tiny island, nearly a dozen Scotch distilleries. My friend ghosted me. Covfefe-19 happened. I didn't go to Scotland. Still, this was supposed to be the year I cut loose a little bit, traveled more, saw more movies in theaters, that sort of thing. Damn this pandemic to the fires of Oblivion.

I have plans to visit Belgium next year with my friend Artemismad Scientist

. For that, I'm learning French. If I feel like I can understand that language, I'll also try to learn some Dutch. As a bonus, that means I could get by in France and the Netherlands also. Yes, I know that a lot of people in all those countries know English. That's no excuse; I refuse to be known as "the ugly American." 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.

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.

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.

So you'll excuse me if dreaming about travel just makes me ranty. I'm generally a stay at home type, but what keeps me going, what keeps me from sinking into the dark depths of depression is a) booze and b) knowing that I can travel to try exotic booze.

At least I still have (a). For now.

The countries I mentioned are not my only desired destinations, but I try not to think of the others, so I'm going to stop myself right here.

As for the prompt, ask me last year and I would have said "Scotland." And I still want to go to the Islay festival at some point, with someone who appreciates the world's greatest whiskey. Or whisky. I forget which countries spell it which way. After a few it won't matter anyway.

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.

And then there's the food. Ever seen the Belgian flag? I'm pretty sure it's a representation of chocolate, beer, and waffles. Belgium is the one country that out-Frenches the French when it comes to cuisine.

But, contrary to popular belief (that I encourage), I can't eat and drink all the time. I'm curating a list of Belgian sites I want to visit. Here are a few:

Musée Hergé, a museum dedicated to Belgium's most famous non-consumable export:
https://www.atlasobscura.com/places/herge-museum

Speaking of Belgian beer:
https://www.atlasobscura.com/places/delirium-cafe

The most metal sculpture in existence:
https://www.atlasobscura.com/places/the-atomium-brussels-belgium

That Damme Canal:
https://www.atlasobscura.com/places/damme-canal

"Yes, I'd like to visit the Hergé museum and also this one. Why are you looking at me like that?"
https://www.atlasobscura.com/places/torture-museum-bruges

Because why not:
https://www.atlasobscura.com/places/tour-cybernetique-cybernetic-tower

"According to this bar, God gave an '11th commandment' to Antwerp: Thou shalt drink beer."
https://www.atlasobscura.com/places/elfde-gebod-eleventh-commandment

Yes, those are all from Atlas Obscura. I have at least a dozen more of them saved. I go to that site when I want to torture myself with dreams of places I can't freaking go to right now.

Grrrr.

Now I'm all depressed again. Maybe I'll open that last bottle of Nocturnum.

8 Like • Comment • View 10 comments

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