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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

October 12, 2020 at 12:04am

#995688

From the Ashes

Entry #6 for

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts February 1!
#2213121 by Elisa the Bunny Stik

politicalwatch@appliancerepairscottsdaleaz.com

I haven't been to Scottsdale, but I've been pretty close.

On one of my excursions, I decided to follow U.S. Route 60 from beginning to end. Or... I suppose it was end to beginning, considering that the US mostly developed east to west, and I was traveling back east.

Route 60 ends just east of the California border, because apparently, a while back, in a transparent attempt to begin its process of secession from the US, it took over the old US routes that ran across it, giving them new designations.

It's not as well-known as the storied Route 66, but I figured, hey, I'm in Vegas and I want to get back to Virginia, and the other end of the old route is in Virginia Beach. So I drove south from Vegas until I reached the end point of U.S. 60 and began the long trek home.

I don't live in Virginia Beach, of course, so this route would take me past my town (missing it by about 35 miles), but I'd long been wanting to trace one of the older, pre-interstate US routes from beginning to end. I have a friend who, until earlier that year, lived on a farm adjacent to Route 60 in Virginia, but that, and Pacific Avenue in Virginia Beach, had been my only experience with that road that I remember.

It's worth mentioning that yes, I'm fully aware that interstates get you where you want to go much faster and with more services available. But I don't travel for the destination; I travel for the experience of traveling.

Still, US 60 through Phoenix was one of the most stressful experiences of my driving career - and I've driven in New York, Boston, DC, LA, Atlanta, and the SF Bay area, just to name a few traffic-heavy places.

Phoenix. Sucked.

A few months after this trip, I saw a news story about a high-speed chase that the cops were involved in through Phoenix. My comment was I didn't believe it, because the top speed you can make through that shithole is, in my experience, approximately half walking speed. Okay, probably it's not a shithole, because clearly people want to live there. But the traffic sucks.

Anyway, the reason I bring this up is that Scottsdale is essentially part of Phoenix. Oh, sure, it has its own separate designation, but my rule is that unless cities are divided by a major river, a significant park, farmland, or a big honkin' wall or something, stop calling them different cities. It's annoying and confusing to anyone who doesn't live there, and I say that as someone who lives in the only state where cities are separate political entities from their surrounding counties.

But U.S. 60 doesn't go through Scottsdale, instead bypassing it to the south. Though "bypassing" doesn't convey the right flavor of traffic jam. After slogging through Phoenix, it was getting dark (I'm pretty sure I entered it in the morning), so I pulled off to spend the night at a motel in Mesa, which is another annoyingly city-that's-not-a-separate-city, directly south of Scottsdale. Or I don't know, maybe it was Tempe. Look, I've only been to Phoenix once and the chance of me being there again is minuscule. Okay, no, maybe it's not; I didn't have time to visit any breweries there, so it's still on my list. I'll just have to remember to allow a few extra weeks to get around the city.

From what I can gather, Scottsdale is, like, the rich people part of Greater Phoenix, so I wouldn't be allowed across the border anyway.

Which does nothing to explain or even hint at an explanation for the actual prompt, so my headcanon is that the appliance repair company is a front for a right-wing conservative pedophile, undocumented immigrant, human trafficking, and opioid distribution ring (hey, they're not the only ones who can make shit up), and that particular email address is for someone who follows the ebb and flow of politics so they'll have some warning when the government decides to start rounding them up.

Though they won't, because the government is in on it.

Following an old US route can get tricky at times, especially when it goes through a city and signs are missing or unclear. I must have looped around Louisville, for example, three times making sure I stayed on track.

And then, when I finally rolled into Virginia Beach a few days later, I stopped for the night just a few blocks short of the other end of Route 60, because that's where my favorite bar in the entire world is located.

Well. Was located. It closed last year, and I'm still sore about it. Add Virginia Beach to the list of cities I have no further reason to return to.

Unless a new brewery opens there, of course.

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