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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 9 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 11 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.

February 12, 2024 at 9:07am

#1064055

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Today, courtesy of Cracked, a brief discussion of one of the greatest movies ever made.

No, ‘Blazing Saddles’ Doesn’t Come With a ‘Trigger Warning’

Mel Brooks’ landmark 1974 comedy Blazing Saddles turns 50 today...

The date on the article is February 7, so as of today, it's fifty years and five days.

In 2024, it’s tough to uncouple the movie from the heated discourse around its place in modern pop culture, namely thanks to the dead horse of an argument that Blazing Saddles “couldn’t be made today” due to its pervasive racist language.

Well, no, it's not that tough. Just enjoy the damn movie and ignore the "heated discourse." Or don't watch it if you don't like that sort of movie.

Not to mention, the conspiracy theory that the radical left is somehow trying to censor Brooks’ film.

Which is amusing since the film is about as radical left as they let you do in the early 70s. For context, when the movie came out, Nixon was still President; he wouldn't resign for another 6 months.

Now, on its golden jubilee anniversary, a lot of people are revisiting Blazing Saddles on streaming, and some folks are outraged to find that it is currently preceded by a “trigger warning” on Max.

Most of the article goes into exactly what that "warning" is: apparently, a three-minute context video.

Which is approximately two minutes and forty-five seconds longer than the "trigger warning" on pretty much every single other piece of professionally-produced entertainment: the MPAA rating or its TV equivalent.

Of course, we have a similar system here on WDC, and I can't count the number of times someone has cried "censorship" over getting their content rating changed. Because your story had the word "fuck" in it and its content rating was raised to 18+ (passive voice there used on purpose), we're obviously offended by that and they've been censored and we're worse than Hitler.

I bring this up only to point out that this sort of thing exists so that audiences have some idea what they're getting into, and to help parents decide what stuff they want their kids watching or reading. If a grown-ass adult decides they don't want anything to do with R rated movies or 18+ rated items here, that's their choice. Wouldn't you rather know you have a choice than, say, be shocked and surprised by a fun cartoon about bunny rabbits suddenly dropping the F-bomb, showing bunnies doing what bunnies do best (making more bunnies), and maybe exploding into fuzzy blobs of goo with long ears?

In short, content ratings and context pieces aren't censorship. Also, pulling your own content because you suddenly had an epiphany that you maybe shouldn't have done that (e.g. the Dr. Seuss books his estate decided were too racist, or Disney pretending Song of the South never existed) isn't censorship.

Back to the movie in question, though, as the article points out, the movie has the bad guys being racist, while the good guys aren't. It's not a celebration of palefaces being able to say the N word. It's a condemnation of it.

And that's not even getting into the other good reason for context explainers: now, 50 years later, there's entire new generations who didn't grow up with Nixon and casual racism, and helping these newer viewers understand history can only be a good thing, since no one pays attention to that shit in school. If it's even taught these days.

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