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 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.

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.

May 15, 2021 at 12:41am

#1010195

In a Red Hood

PROMPT May 15th

Many fairy tales are often based in truth. Research the true story behind your favorite fairy tale and share it with your readers. What lesson or warning was the tale trying to impart?

I don't really have a favorite fairy tale. All the ones I can think of have stupid moral messages, like "don't be curious" or "wives should be submissive" or "never try to rise above your station in life."

And the line between fairy tale, myth, and religious text is, as far as I'm concerned, so faint as to be nonexistent, but I'm not interested in offending anyone.

I wrote about fairy tales in general in here about a month ago: "Wagging Tales"

. That entry was more about how these stories might have truly ancient origins, some possibly dating back to a time before writing. So I would expect that, in many cases, the kernel of truth that might have originally spawned the tale is lost in the mists of time.

As for lessons or warnings, I have a habit of finding the "wrong" meaning in a lot of stories. It's kind of a hobby of mine. Why, just yesterday, NaNoNette

wrote a newsfeed post about finding a decent translation of Oedipus. The note is here if you want to see it: "Note: I just read Oedipus Rex and Antigone. The 1982 tra...". Now, the story of Oedipus isn't what most people would call a fairy tale, but it's a story with a moral that presumably appealed to its original Greek audience. It occurred to me, however, that the bad things that happen in that story would never have happened had the Greek roads been wide enough to let Oedipus pass his (he didn't know it was his) father without them getting into a fight and Oedipus committing inadvertent patricide. The Greeks probably saw something about hubris, or the futility of avoiding prophecy, or the need to take responsibility for one's actions however inadvertent they might be, or whatever they saw in the story. Me? I said that the real problem was if you don't invest in infrastructure, there will be tragedy.

So, okay, actual fairy tales. I suppose Little Red Riding Hood qualifies. There are a bunch of different versions, though. In some of them, Red has agency; in others, not so much. This likely reflects different cultures' ideas about how passive little girls should be. The one I generally remember has a woodsman (aka a Mighty Male Hero) coming to her rescue.

Thing is, though, I could never find any allusion to that tale having its roots in a true story. Likely, it's more allegorical - which is fine, because often, allegories illuminate deeper truths. My favored interpretation is that, as with the one about the frog-kissing princess, it's about the transition from the innocence of childhood to the realities of adulthood. There's also some talk about it being a repurposed Norse myth, which of course involved Loki pulling one of his usual trickster god tricks.

Myths, of course, often also come from true stories, but again, those stories tend to get lost in time.

If I were rebooting the LRRH story today, though, I'd change the ending. No woodsman, or if there is one, he's the actual bad guy, and the Wolf would turn the tables on him and maybe wear his skin as a trophy. Turns out the Wolf only killed Grandma because Grandma was plotting to drink Red's blood in an attempt to gain immortality, and the whole façade of Wolf scaring the hell out of Red is a lesson for Red in not trusting people simply because they look like sweet, innocent old ladies.

And then Red and the Wolf trot off into the woods together to live happily ever after.

The better to eat you with, my dear.

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