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 11 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.

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.

March 18, 2022 at 12:03am

#1029114

Poe Dunk

Now it's time to once again talk about one of my literary spirit guides.

How to Deal with Rejection (and Get Revenge) Like Edgar Allan Poe
Catherine Baab-Muguira on Doubling Down on Your Ambitions

Before we get into it, this is essentially a book ad. I've already stated, numerous times, my opinion on that. But for those with other opinions, I issue this disclaimer.

When Edgar Allan Poe was 17 years old, he and John Allan loaded up the family station wagon with all his clothes, posters, and books, and made the 70-mile trek west to Charlottesville, Virginia.

In the interest of clarity, I will point out that this journey was 200 years ago. These days, I make that trip pretty regularly (or did, in the Before Time, when I had a car) and it takes about an hour. The author here is being deliberately modern, I think, but I'm pretty sure horses were involved in the journey, a "station wagon" was something else entirely, it was probably muddy, and it took a bit more than an hour.

Also, it's northwest, not west. Look at a map.

Among the rolling hills of that town, Thomas Jefferson had recently founded a university meant to serve the sons of the state—at least, those sons who could afford to spend a few years drinking, gambling, goofing off, and, on occasion, attending the odd lecture, maybe sitting an exam or two.

Not much has changed in 200 years. More out-of-state students, but the rest is pretty much the same.

Writing to Poe’s brother Henry in 1824, John Allan pointedly referred to Rosalie as “half your Sister,” adding piously, in case his point was somehow missed, “God forbid my dear Henry that We should visit upon the living the Errors & frailties of the dead.”

I consider that fairly progressive for the time. Considering that at the time, some people owned other people.

You know how it goes. You’re on your own for the first time. You don’t want to admit how lost you are, don’t want to beg or turn back the way you came. And so, to cover the widening gap between your means and your expenses, you start to borrow. If there had been, in those days, credit-card company reps loitering outside the UVA student union with their quills and free waistcoats, Poe would have signed up on the spot.

Those bastards helped me fuck up my twenties. Notice how I accept the brunt of the blame. But they enabled.

After a few hands, he found himself in an even bigger hole, so he just kept on playing and losing, and losing, and losing, until he was $2,000 in hock—some $50,000 in today’s money.

Now he really couldn’t stay in Charlottesville. There was nothing for it but to trudge home, tail between his legs, creditors nipping at his heels.

You can still visit the room where Poe stayed while at UVA. It's a couple miles from where I'm sitting. As with so many other historical sites, given that he wouldn't achieve fame for many more years, it's uncertain whether the official room is the actual room. But whatever; it's worth a visit anyway.

Anyway, that's even more debt than I had incurred. And that's without credit cards.

The excerpt goes on to detail Poe's return to Richmond and rejection by his foster father, which caused him to once again leave Richmond and become... well... Poe.

Yet all of us will face rejection at some point. No one is exempt, which makes it all the more important that you understand how to have the right response—that, no matter your age or exact situation, you harness the gut-searing motivation that rejection can provide you, and make an ardent resolution like Poe himself made. “If you determine to abandon me,” he ranted to Allan in another letter later that year, “I will be doubly ambitious, & the world shall hear of the son whom you have thought unworthy of your notice.”

Translation: The best revenge is living well, and, as per the old Klingon proverb, "Revenge is a dish best served cold." (Gagh, on the other hand, is a dish best served still squirming.)

But you don’t have to mirror Poe’s exact playbook, which involved hopping a ship from Richmond to Boston, Massachusetts, assuming an alias, and, while starving and struggling to find work, paying out of his own pocket to publish his first book of poems, Tamerlane. You just need to nail the larger moves, outlined below.

Boston? Hell no. It's cold in Boston. Even colder than Richmond. Even colder than the shoulder John Allan turned to Edgar.

Step 1.
Decide on revenge-via-success

You’re gifting yourself a huge sense of purpose at a moment when you might otherwise be floundering, rudderless. So screw your heart up tight. Suck in your breath. Swear to yourself that one day they—whoever “they” are—will rue the day they doubted you.

Yeah, I don't know. The old "find dirt on them and leak it to the media" trick is satisfying, too.

Step 2.
Change addresses in a big way

Think of those who’ve come before you and take heart. Generations of theater kids, queer kids, artists, intellectuals, freaks, and dissidents of all stripes have all left their hometowns for bigger arenas. Buddha did it, so did Jesus. Poe too. Why not you?

Because I'm not Buddha, Jesus, or Poe?

Still, I can't help but recommending travel for anyone who wants to write, or even just experience something new.

And that's about it for the excerpt. Mostly, I just wanted to share the link. I don't know if I'll buy the book, but it seems well-written.

Just remember, follow all of this advice and you, too, can be found dead on the streets of Baltimore someday.

Speaking of Poe, I went to see a movie that owes a lot of its existence to him.

One-Sentence Movie Review: The Batman

Battinson is a more effective Batman than I'd expected, the set designs and costumes are excellent, and the action is terrific; however, the plot is unnecessarily convoluted, and like so many other movies, it's probably longer than it really needed to be -- but my lifelong crush on Catwoman continues, so I'm glad I saw it.

Rating: 3.5/5

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