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').

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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.

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

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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

September 22, 2023 at 8:40am

#1056063

Let's Visit Spook-ane

Well, here's a source I don't think I've quoted before: Architectural Digest.

9 Creepiest Places You Should Probably Never Visit
From an abandoned asylum to a church adorned with human skulls, these sites are not for the faint of heart

Dude. I've spent the night at the Clown Motel

in Tonopah, Nevada. You think these, or any, locations can faze me after that? Except for, you know, actual dangerous places like active volcanoes or Baltimore.

Article is from October (hence the theme) of 2019, but I doubt if much has changed.

Though popular attractions, these creepy places have the benefit of being rooted in history with layers of culture, which means they’ve been well preserved over time.

That also means maybe don't use other cultures for cheap thrills without their permission.

Instead, these are places packed with bones, scrawny cats, and the paranormal.

Bones are just part of the life cycle. I hope the kitties are okay. And the paranormal is all in your head.

Now, remember, for full effect, you'll need to click on the link for helpful pictures.

Island of the Dolls, Mexico

Somehow, I doubt that's its official Mexican name.

Isla de las Muñecas, as it's called in Spanish, is south of Mexico City...

Or that city name, for that matter.

...the island is largely deserted, save for hundreds of dolls hanging in the trees...

Gosh, I wonder why. Now, would someone please bet me lots of money that I can't spend the night there?

Mansfield Reformatory, Ohio

Oh gods, no! Not Ohio!

It's no longer in operation—it closed in 1990—but you can go on a guided or self-guided tour...

Alone.

Nagoro, Japan

Small-town Japan is quaint, but this eerie village in the Iya Valley has just 30 residents—and over 400 large dolls.

Again with the dolls. Though I'm pretty sure these are technically mannequins.

La Recoleta Cemetery, Buenos Aires, Argentina

At least they tried to get the language right, this time.

...this Buenos Aires resting place is seriously haunted—even the city's tourism website endorses the Neo-Gothic cemetery’s status.

How much you wanna bet the city had some giggling workers put in speakers and animatronics on the sly?

Trans-Allegheny Lunatic Asylum, West Virginia

The hospital earned National Historic Landmark status in 1990 but closed down in 1994—and rumored ghosts have haunted the premises ever since.

Oh, fun! Not just ghosts, but batshit hillbilly ghosts!

Sedlec Ossuary, Kutná Hora, Czech Republic

The design dates back to 1870, when a local man was hired to take bones stored in a crypt and turn them into art.

I might have to go Czech this out.

Veijo Rönkkönen, Finland

Named for the artist who created the 550 concrete sculptures within—all human figures in a forested setting—it can appear overwhelming, as if you are being watched or maybe even judged.

Basically, more dolls.

The Hill of Crosses, Lithuania

Based on the picture in the article, this is actually pretty cool.

Akodessewa Fetish Market, Togo

...just keep in mind that "fetish" has at least three meanings, and this is one of the less salacious ones. Still, the appropriate definition here includes the phrase "believed to be inhabited by a spirit," so, you know... good luck.

So, by my quick scan, there's at least one of these on every continent, save for Antarctica and Australia. Way to be inclusive, guys. Antarctica's probably left out because there's just not much there, and Australia because, well, that whole continent/island is creepy.

I'd visit all of them. Wouldn't you?

4 Like • Comment • View 5 comments

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