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 10 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 12 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.

February 23, 2024 at 10:28am

#1064737

Coming Up the Pike

My penultimate effort for February's "Journalistic Intentions"

[18+]...

Pike

In the original Star Trek series, James Kirk was the captain of the Enterprise. Everyone knows that. If the Sentinelese ever decide to stop killing everyone who sets foot on their island, and decide to join the rest of the world in peaceful harmony, we'd be all like, "Cool. Cool. One question: who's the captain of the original Enterprise?" And they'd be like, "Jim Kirk."

But that's not how it was supposed to go. The original pilot episode featured a Spock who wasn't emotionless, a Majel Barrett character who was, and a captain named Pike. (Roddenberry probably thought one-syllable names containing hard consonants were more "manly," which is amusing coming from a guy named Roddenberry.)

Most people with even a casual interest in Trek know this, too, because they reused the pilot for scenes in a two-part episode, thus cementing it as canon in the future history they created. It's even canon, in a different way, in the alternate universe that was J.J. Abrams' fault.

The first guy who portrayed Christopher Pike was Jeffrey Hunter, which, to be fair, would also make a great name for a square-jawed starship captain. Later, a prequel series would feature a captain named Jonathan Archer, which is close enough.

Sad story about Hunter, though. He turned down further work in Trek, wanting to concentrate on his film work or whatever. Reasonable decision for an actor, I suppose. But in 1968, while working on a movie, Hunter got injured in an on-set explosion. A few months later, before the original series aired its last episode, he died of a maybe-related cause.

If he'd stayed with Trek, that probably wouldn't have happened. But then, we wouldn't have William Shatner to make fun of, or the Spock who has become a cultural icon, or, and I cannot emphasize this enough, the utter awesomeness that is the Trek series Strange New Worlds, a prequel to the original series with Anson Mount as Captain Pike.

It's because of Anson Mount that when some nerd asks me "Kirk or Picard," I can no longer answer "Trick question. It's Sisko." Nope. Chris Pike all the way.

3 Like • Comment • View 2 comments

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