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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QPdoll

about 13 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

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Wordsmitty ✍️

about 16 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

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Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

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Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

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WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

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Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

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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?

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