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!

a day 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.

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Adherennium Plotting something

a day 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.

June 10, 2019 at 12:11am

#960495

Grilled

This week's theme is simple...you're having a backyard barbecue. For Monday's entry, what meats, side dishes, and beverages are you serving? Do you have a go-to dish you like to prepare?

I used to do the backyard-barbecue thing. Well, technically, it's a back deck barbecue thing; my backyard is 90% poison ivy and 10% snakes in the weeds. Yard work is, well, work, which I'm just as allergic to as I am to poison ivy. Plus, it's... outdoors [shudder].

But now, as a single man who's working on weight loss, my grill sits covered and neglected. At this point, there's probably spiders under there somewhere. I don't mind spiders, but I also don't want to put my hand into a web of the little fuckers. It's not worth it to mess with the grill for a mere 2-3 ounces of food; I could grill a bunch and stick the bulk in the fridge for later, but what's the point? Reheated grill food is crap.

Let's make one thing clear, though: when I did barbecue, it was definitely meat. Not zucchini. I hate zucchini. Well, that's not fair; I'll eat zucchini if it's properly prepared; at least I consider it food, unlike eggplant. Eggplant (that's aubergine for you folks across the pond) isn't actually food. It has a nice purple color, though. Apparently, it's a popular emoji. I don't understand why. I don't speak emoji. You know what's really good grilled, though? Asparagus. If you like asparagus. I used to have a special pan to hold it on the grill.

Anyway, meat. Before you go, "Well, no wonder you're trying to lose weight," understand that the problem with meat isn't the meat; it's the fat. I only ever liked lean meats. Plus bacon, and you have to basically do yoga to cook bacon properly on a grill, because the process is so convoluted.

So for grilling, I was always an old-school purist. Steak - preferably filet mignon (I have expensive tastes, in case you haven't noticed) - or chicken, minimally marinated, in small quantities. I've done burgers too, of course, but those little bastards like to fall through the grill slats; they're a pain in the ass. For the side, well, corn of course (that's maize for you Brits - this language barrier is a pain in the arse, too).

As for drinks, well, beer, of course. And not the horse piss they sell by the case at convenience stores, either. I'd go to one of our many local breweries or taphouses and fill a growler or five with whatever interesting brew they have available. Or, well, wine will do, also.

Really, teetotalers, gluten-freeks, and people with veganism or other eating disorders might not appreciate my barbecues.

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