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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
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

January 14, 2019 at 12:38am

#949599

The Apprentice

“We are all apprentices in a craft where no one ever becomes a master.” -Ernest Hemingway

What are your thoughts on this quote by a writer many consider a master? Who are some other writers you admire or consider masters?

There's a joke floating out there somewhere that riffs on the old "Why did the chicken cross the road?" riddle.

One of the answers is:

Ernest Hemingway: "To die. In the rain."

One of the first things I noticed about Hemingway when I was forced to read him (and make no mistake, I had to be forced) was the forcefulness and brevity of his words. The chicken joke is spot on in that regard. I mean, look at the title of "The Old Man and the Sea." Six words, each one syllable, each exactly three letters, and it perfectly sums up the book.

Too bad the rest of the book is the equivalent of watching grass grow.

I mean, would it be as popular a book to torture high school students with if the title had been something like "A Senior Citizen Attempts to Catch a Fucking Marlin?"

In fact, Hemingway's bluntness is so infamous that I have to doubt the above quote can actually be ascribed to him. I mean, "apprentices" is four syllables, which is three more than he prefers to elucidate.

Look, here's the thing: I'm not a fan of "literature." About the only classic author I can stomach is Mark Twain. That guy is still freakin' hilarious after more than a century. I mean, just feast your eyes upon this utter smackdown of James Fenimore Cooper (as well as his fans), first penned in 1895:

http://twain.lib.virginia.edu/projects/rissetto/offense.html

It seems to me that it was far from right for the Professor of English Literature at Yale, the Professor of English Literature in Columbia, and Wilkie Collins to deliver opinions on Cooper's literature without having read some of it. It would have been much more decorous to keep silent and let persons talk who have read Cooper.

Cooper's art has some defects. In one place in "Deerslayer," and in the restricted space of two-thirds of a page, Cooper has scored 114 offenses against literary art out of a possible 115. It breaks the record.

No, seriously, I'm not kidding. Go read the whole thing. It's pretty short, and it's worth reading every word. Though it takes me twice as long to read it as it probably should, because it cracks me right up every single time.

That said, whoever penned that quote up top attributed to Hemingway (and I am willing to admit, grudgingly, that it might have been actually Hemingway) did get it right, in my opinion: There is no writer so great that he or she cannot improve. At some point, though, it becomes a matter of personal taste. No amount of convincing will get me to believe, for instance, that James Joyce was anything other than the literary equivalent of Jackson Pollack: splattering words around his paper canvas like bright paint, their arrangement so random that people see what patterns they want to see in it.

At least with Pollack, I can glance at a splatter painting for a brief moment, utter a dismissive "Bah!" and move on. Reading takes actual time.

But I digress. Point is, I'd rather read a good comic book than slog through another neurotic "literary" excrementation.

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