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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Brandiwyn🎶

a day ago
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').

1 Like

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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

June 29, 2023 at 9:27am

#1051820

Occupational Hazards

The headline from today's article sounds like something Cracked would tackle, but no, it's LitHub.

6 Famous Writers Injured While Writing
When Making Stuff is Hazardous to Your Health

You'd think that out of all possible professions, writing would be among the least prone to occupational hazard. Maybe the occasional carpal tunnel, but that's about it, right? Well, you'd be right, but as this article shows, nothing is perfectly safe.

Even the toughest of poets and strongest of Hemingways would have to admit that “writer” is not a particularly dangerous job. (Unlike, say, fisherman, miner, logger, knife-thrower assistant.)

This, of course, depends on the kind of writer you are. Novelist who sits at home and relies on Wikipedia for research? Sure. War correspondent? Not so much.

Still, a few writers in history have actually suffered some serious health problems as a result of their writing practice—or in some cases, the drugs they used to fuel it.

Yeah, drugs probably shouldn't count. Those aren't specific to the writing profession.

As I noted above, this isn't Cracked, so no numbered list, countdown or otherwise.

Orwell struggled with health problems from childhood, and things were not improved when he was shot in the neck in Spain. But as Ross writes at PW, “his health collapsed for the first time after the writing of Homage to Catalonia, and the heroic effort of writing and revising Nineteen Eighty-Four would kill him.”

Or was it the government trying to suppress his work?

Over at Poets & Writers, Anelise Chen notes that Herman Melville “dove with such intensity into his whale book that his entire family circulated letters conspiring to make him rest. Ignoring their pleas, he emerged from Moby-Dick plagued with eye spasms, anxiety attacks, and debilitating back pain.”

What a coincidence. Those things happen when you try to read it, too.

The nineteenth-century Italian poet Giacomo Leopardi...

Who?

...whom Adam Kirsh has dubbed “the supreme poet of passive, helpless suffering,”...

Clearly, Kirsh didn't know Leonard Cohen.

...may have turned out that way because he from debilitating scoliosis, which gave him a hump and turned him into, as he put it, “a walking sepulcher.” He blamed his condition on his “scholarly excesses”

Nah, it was all the sex he got from being a poet.

Honoré de Balzac was famously addicted to coffee, which he loved for what it did for his writing.

Take heed, fellow WDC authors.

Neither did it go perfectly well for Balzac himself, who reportedly died of caffeine poisoning at the age of 51.

Fuck me, caffeine poisoning is a thing?

Objectivist Ayn Rand also had an addiction that sprang from her writing process: amphetamines.

Unfortunately for the world, they didn't cause her early demise.

If you’re familiar with his work, it isn’t particularly surprising to find out that Franz Kafka put himself through emotional and physical hell to get his writing done.

What? That's absurd.

His throat closed up, precluding the ingestion of any food, and so he technically died of starvation, working on his story “The Hunger Artist” to the very last.

Thus was the modern definition of irony born.

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