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Thursday, May. 23, 2024

8:51pm EDT

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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

a day ago
In response to "More Science"

Giggles. Thank you for the laugh- especially this phrase, "I always picture Doc Brown's workshop in Back to the Future. Yes, of course I know it's wrong, but I'd rather be amused than right."

1 Like

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

January 30, 2022 at 12:18am

#1025659

The Fix

Only two left from "JAFBG"

[XGC]. After this, only one. Which I may or may not be able to post at the usual time.

Global supply chain issues. Is it a labor shortage, wage shortage, something else? How do we fix it?

Hell if I know.

I'm not even sure it needs to be "fixed." Not that it isn't inconvenient, but if we could fix everything that was inconvenient, we'd... you know, actually, that would be awesome. Get right on that.

I say that because these things tend to sort themselves out. Either we get shit moving again, or, if we don't, we get used to it.

As for the labor shortage / wage shortage thing... well, anything I say about that will be political. So I'm going to say it anyway: you want people to work, pay them more. If you want businesses to pay people more, don't be surprised when inflation happens. If people start getting paid better, and then inflation happens, don't be surprised when they end up being paid the same, adjusted for inflation, as they were before they got paid more. The system pretty much requires that some people be paid dogshit wages so the rest of us aren't inconvenienced. Don't like it? Change the system... or at least try not to be one of those getting dogshit wages.

Of course, it's not just about being paid more. It's also about not being treated like shit at work. I'm glad workers are finally starting to get the upper hand, because managers have become too complacent in thinking that they can do whatever they want and the peons will come to work anyway because they have no other choice. Well, now they have a choice. Just know that every time someone complains, "No one wants to work," what they're really saying is: "No one wants to work for me (because I'm an asshole)."

One thing I'm certain of, though, is the people who said that the exploited workers would come begging for their shit jobs back once stimulus ended were, obviously, completely wrong. Because it ended, and people are still not interested in working at your soul-deadening, productivity-optimized, unpredictable-schedule, doing-the-work-of-three-people, no-chance-for-promotion craphole business.

Don't get me wrong; I'd like to see the supply chain problems improve because I've been holding off on buying a car and a new laptop, both of which require computer chips that I hear are still in short supply. But I'm patient.

So far.

7 Like • Comment • View 4 comments

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