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

November 9, 2020 at 12:02am

#997949

Sproing!

It could be argued that everything I own fits this prompt.

PROMPT November 9th

Write about something you own that is weird, wacky, or downright silly. Where did you get it and what significance does it hold for you?

Everything... or nothing, since a collection of weird things becomes, by definition, normal.

When I was a kid, I loved Mad Magazine. I owe that era a debt of gratitude for my taste (well, actually, lack thereof) in comedy and parody.

Many of the features seem childish today, even for me, but Preteen Me couldn't get enough of that dreck. Various artists, known collectively as "The Usual Gang of Idiots," as I recall, each had his own idiosyncratic style, much as a lot of the funny comic strips and cartoons you find on the internet today do.

Mad's chief rival in the adolescent-boy market was Cracked, a magazine that just couldn't measure up to Mad's high standards, which is, of course, saying something. Nowadays, of course, Mad is but a pale shadow of its former self, and Cracked , in a completely different format, is one of the funniest things on the internet... sometimes.

It's notable that Mad, for all of its juvenile humor, was primarily written and illustrated by grown-ass men, which either says something about boys or something about men -- or, possibly, about anyone who possesses a Y chromosome of any age. When I got a bit older and graduated to Playboy, I remember they once had an interview with Jay Leno (yes, I did indeed read the articles). This was before he took over the Tonight Show, if my memory serves me (which it often doesn't). In the interview, they asked Leno, "What do you think is the primary difference between men and women?"

And Jay replied with something like, "The primary difference between men and women is that all men love the Three Stooges, and all women think they're shitheads."

That stuck with me in the way that all profound philosophy does.

One of the weirdest, most elegantly and inherently funny cartoonists for Mad was Don Martin.

He was active at the magazine between 1956 and 1987, which meant I got to see his work at its peak. If it's possible to put physical comedy (in the vein of The Three Stooges) into the form of drawings, Martin was the guy who did it. His style appeared simple, and was often accompanied by brilliantly inked and perfectly onomatopoeic sound effects, much like the campy 1960s Batman TV show. These sound effects made me laugh. Every. Damn. Time.

Martin died in 2000, and after, someone collected his Mad works into a two-volume hardcover collection, which I display proudly near my three-volume Complete Calvin and Hobbes. While the latter has the distinction of almost killing me from bouts of laughter at times -- the C&H snowmen strips in particular have never been, are never, and will never be not funny -- Martin's consistent, if puerile, genius spanned a much longer period of time, reflecting the evolution of comedy and pop culture over three entire decades.

No, I don't remember how I acquired the collection. I probably ordered it on the Internet, though a search through my nearly 25 years of Amazon purchases came up as empty as the collection of fucks I have left to give. I only mention this because "where did you get it" is part of the prompt, but my memory for that sort of thing isn't nearly as good as my memory for Don Martin's irreverent comic drawings.

Now, I have zero talent for drawing, myself, and whether or not I have any ability in comedy is as open a question now as it was when I first tried my hand at it as a teen. But this Don Martin collection is one of my most prized possessions not only for its nostalgic value, but because it's just so damn timelessly funny. And it's good to know that, in times of stress or our impending descent into irreversible chaos, there's one thing (okay, two things if you count the C&H collection) that will never fail to make me laugh.

And I gotta laugh.

Some samples of Martin's work:

https://i0.wp.com/www.dailycartoonist.com/wp-content/uploads/2020/03/sounds-don-...
https://www.lambiek.net/artists/image/m/martin_don/martin_don_ono.jpg
https://i.pinimg.com/originals/37/44/0c/37440ce89af164301766ed44a3a5fc39.jpg
https://www.madmagazine.com/sites/default/files/MAD-Magazine-Don-Martin-Evening-...

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