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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

14 minutes ago
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 20, 2019 at 12:46am

#950038

Historical Witness

What event from history do you wish you could have witnessed?

So many options...

I'll assume here that I'd be a kind of fly on the wall - unobserved myself, unable to affect anything, and unable to be affected by anything other than photons and sound waves. I mean, what's the point in observing if you can't observe? I'm also thinking this means singular events, not protracted ones such as wars.

This means that I wouldn't be able to pre-emptively kill anyone whose impact on history is negative, like the classic Hitler or the pure evil of Carrie Nation.

So, the first thought that came to mind was to observe the first moon landing (as per above, I'd be unaffected by the extreme heat or vacuum). It was, after all, not only the most significant thing we've ever done as a species, but the most significant thing I can imagine doing (we might set foot on other worlds in the future, but the moon was the first). Then I'd be able to tell all the retards who think the event was faked that it wasn't. But then I realized - these people are retards. They wouldn't believe me, anyway, any more than they do now. They're not worth my time, and besides, the event was well-documented anyway.

That got me thinking about conspiracy "theories," so of course the next thing I thought of was the assassination of JFK. But that's depressing, and besides, there were already hundreds of witnesses as well as video footage, and there's still controversy surrounding it, so why would I expect to see what actually happened any more than anyone else there? Besides, again, no one would believe me, so I'd only be indulging my own curiosity - and honestly, I'm not that curious about it.

Consequently, I figure it needs to be something that I'm personally curious about, but feel no need to share with others. If I take "history" literally, I'd be limited to the past 10,000 years or so; before then, there were no written records - hence, "prehistory." A shame, because I think it'd be fun to observe the presumed impact event that ended up wiping out most of the dinosaurs, or the moment some human first tamed fire.

Then there are the events that supposedly took place during historical times, but are of questionable historicity and/or the subject of contradictory accounts: Washington chopping down the cherry tree, the birth or death of Jesus, Alexander cutting the Gordian Knot, etc. Those are cans of worms I don't really feel like opening; again, we run into the idea that I'd have to satisfy my personal curiosity without feeling the need to convince others of what I saw/heard. Or didn't see or hear, in these cases. At some point, it doesn't matter whether an event really happened or not; it makes no difference to how we think about it.

So I think it depends on when you ask me. I'd have had a different answer last year, and will probably have a different answer next year. Hell, I'll probably have a different answer tomorrow. But right now, today, this article caught my eye, as it concerns two of my most favored historical figures:

https://theculturetrip.com/north-america/usa/new-york/articles/what-you-need-to-...

Given his longevity, bookishness, and outstanding oddness, it’s not terribly surprising that one of Tesla’s few friends was the writer Samuel Langhorne Clemens, alias Mark Twain.

Having met at a New York social club to which both men belonged, Mark Twain credited Tesla with curing his debilitating constipating[sic] with an oscillator that vibrated his bowels until he narrowly made it to the restroom in time to experience his remedy.

That. I'd pay to see that.

4 Like • Comment • View 5 comments

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