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Monday, May. 20, 2024

5:37am 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

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

January 22, 2024 at 10:29am

#1062791

For Short Values of 'Lifetime'

A little perspective, from Cracked...

5 ‘Once in a Lifetime’ Events That Are Actually A Lot More Frequent Than Once in a Lifetime

I'll just jump into the list, which, naturally, counts down.

5. Catching A Foul Ball

Sure, it’s no home run ball, but catching a foul ball while watching a live baseball game is still a nice consolation prize.

Judging from some of the videos I've seen, there's more competition, with fewer rules, between the spectators near the end of the ball's trajectory than there is on the field.

The fact is, though, that if you’re a frequent attendee, especially if you’re picking seats based on likely trajectories, the odds really aren’t that astronomical. They basically sit right around 1 in 580.

Hell of an "if" there. I haven't been to a baseball game as a spectator since Nixon was president. Hell, I've played it more than I've watched it. I guarantee you me catching a foul ball would not only be a once-in-a-lifetime experience, but a probability-breaking macroquantum event.

4. Total Solar Eclipse

Would it surprise you I knew about this one? No? Okay.

It’s true. The belief that it’s so incredibly rare is probably based on the fact that it takes 375 years to happen again in the same location. If you’ve got a deep love for orbs and an even deeper bank account, though, you could see dozens in your lifetime with the right travel plans.

Yeah, but let's not confuse "happens somewhere on Earth" with "happens where you live." Tell you what, though, if you live around Paducah, Kentucky, you experienced totality in 2017, and will do so again this April. So you're, you know. Doomed.

3. Animals Going Extinct

The fact is, animals are going extinct constantly, in huge numbers. The reason we don’t see more coverage of each particular critter configuration we’re losing isn’t because it’s not happening, it’s because there are literally too many to report on without their own 24-hour news cycle.

2. Blue Moons

I'll give them points for not explicitly stating the false definition here. But they did include a link to a site that still promulgates that mistake, so negative points for that. By the false definition, a few years ago, we had one in January and one in March. That can never happen with the true definition.

The actual last Blue Moon was on August 22, 2021. The next one is this year, on August 19. After that, May 20, 2027. One can only occur in August, November, February, or May. But yeah, they happen every 2-3 years. Which is rare enough to warrant the "once in a blue moon" expression, but the false Blue Moon can never, ever coincide with the true Blue Moon.

To mash up two entries into one fun fact to throw into bar conversation, “once every total solar eclipse” would actually be more frequent than “once in a blue moon.”

Again, sure, if you're privileged enough to be able to travel to the eclipse.

1. Investment Opportunities

And this one should go without saying.

If someone wants you to buy what they're selling, it's because they think your money is worth more than what they're selling. You should probably think so, too. Which should be obvious, but greed can blind you.

3 Like • Comment • View 1 comment

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