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!

about 6 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 8 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.

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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.

January 9, 2022 at 12:03am

#1024391

Hell, or The Matrix?

Courtesy of "JAFBG"

[XGC]...

Hell is actually just a waiting room where your least favorite song plays on repeat for eternity. What song is playing?

"Simply Having A Wonderful Christmastime."

Bad enough that it's banal. Worse that it's repetitive. But what makes this song the dark nadir of the universe is that it oozed from the pen of one of the greatest songwriters of all time, someone who ought to have known better than to foist this musical mayonnaise sandwich on an adoring world, a world that expected greatnesses like "Blackbird" and "Live and Let Die," or any number of other songs with some bite to them.

And just to forestall any comments along these lines, no, the song is certainly not about people practicing witchcraft and, unexpectedly interrupted, having to hide their athames, pentagrams, and wands behind their backs, whistle innocently and go, "eh, heh, hum, simply having a wonderful Christmastime, yep, that's all, nothing but Christmas here yes sirree" That's a stupid urban legend probably made up to try to give this shallow pablum the illusion of depth. Yes, that is an actual rumor that someone started. Considering that someone back in the 60s started the rumor that the original Paul McCartney is dead and this one is his doppelganger replacement... you know, actually, that might explain the utter crapitude of the song. But no. No. Stop it.

In any case, I'm saying this with the holiday music loop season not far behind us. Ask me another time and I'd probably pick a different song. Anyway, if there were a hell, the prospect of listening to one song -- any song -- on endless loop would scare me straight more than the traditional fiery brimstone and eternal flaying or whatever it's supposed to be.

One-Sentence Movie Review: The Matrix Resurrections:

With plenty of the visually intriguing action scenes and special effects that these movies are known for, and in spite of its interludes of explanatory dialogue that will surely provide fuel for countless amateur sophomoric philosophy discussions (mostly while stoned), the movie actually moves along quite nicely, if you ignore silly things like the plot -- John WickNeo does spend an inordinate amount of time trying to resist his calling, much as he did way back in the first movie; however, it's worth watching just for its slew of sly, self-aware meta-references.

Rating: 3/5

6 Like • Comment • View 6 comments

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