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

November 23, 2022 at 12:02am

#1040944

To Die Laughing

This one's been hanging out in my queue since October, but whatever. Poe is timeless.

The Edgar Allan Poe Murder Conspiracy

Article is from Cracked, so take it with a grain of gothic black salt.

As the original goth boi, it’s only fitting that Edgar Allan Poe’s death was as mysterious and haunting as one of his stories. Just before he died at age 40, he seemed to drop off the face of the Earth for a week, and his death has been attributed to everything from low blood sugar to murder.

There was a movie called The Raven about 10 years ago, starring John Cusack as Poe. Critically panned and engendering lukewarm audience response at best, I felt like it was severely underrated. Not that it was a great movie, but it didn't suck, either. I think most people missed the point. The movie makes the most sense, I think, if you remember the Poe quote, "All that we see or seem is but a dream within a dream." Or maybe I'm enough of a fan of both Poe and Cusack to have enjoyed it anyway.

15. Missing Poe-son

Oh, how clever. A Poe pun. Well, I shouldn't complain too much; I have every intention of adopting a tomcat just so I can name him Edgar Allan Purr. Bonus points if I can find a black one.

On September 27, 1849, Poe left Richmond, Virginia, where he’d been busy talking his childhood sweetheart into marrying him, for Philadelphia for a job editing a poetry collection (it needed more symbolism or something), after which he intended to head back to New York, where he lived.

Lots of places claim Poe, and for good reason. He belongs to everywhere, but really, he was a Virginian.

14. October 3, 1849

Four days before his death, Poe resurfaced in Baltimore, if you can call the gutter a surface.

Isn't that just basically Baltimore?

13. Poe’s Death

According to the most likely account, he never got it together long enough to explain how a business trip turned into a disoriented game of dress-up before he died on October 7.

Of course it was October.

For we knew not the month was October,
And we marked not the night of the year

12. Poe’s Cause of Death

Cracked's attempts to fit this story into its usual bite-sized countdown chunks seems forced here, so I'm skipping a few; basically, the next several points involve the various ideas about what might have led to his death. There are a lot of them, and as far as I can tell, none of them really fit.

My personal theory? He fell ill from gothic ennui.

The only person who saw Poe alive after he was brought to the hospital was Dr. John Moran, who kept changing his story.

Keep writing unreliable narrators

and you, too, can have your last days confounded by an unreliable narrator.

You know what would be really helpful here? An autopsy. A death certificate. Any records of any kind. None have survived, if they ever existed, and no autopsy was ever performed on a famous writer who died a bizarrely mysterious death. We don’t know, guys. Our money’s on the hospital administration.

Well, this is America we're talking about. Most likely he died of shock after seeing the hospital bill.

To die laughing must be the most glorious of all glorious deaths!
—E. A. Poe

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