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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:

Kåre Enga in Udon Thani

a day ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

a day ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

a day ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

a day ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

May 28, 2021 at 12:02am

#1010894

Fail

PROMPT May 28th

What would you do if you knew you could not fail?

Fly.

No, I don't mean go over to the airfield and take piloting lessons. I could have done that before, given enough time and money. I just couldn't be arsed. I'm talking about whooshing through the atmosphere, like Superman or whatever.

I mean, if I can't fail, that mans I'd be able to soar under my own power, right?

There are levels of failing. Trying to fly and failing could, depending on the circumstances, be fatal. "Oh, I'll just jump off this cliff and trust that I'll miss the ground below entirely." Trying to get a pilot's license, on the other hand, like I said, just takes time and money... along with a visual acuity that I no longer have, so that's right out at the moment. But even absent the vision problems, the thing stopping me has not been fear of failing (or crashing), or lack of funds (it's really not much more of an investment than many other lessons, unless you actually buy an airplane), or even lack of time. No, it's that I have no purpose for it other than being able to say "I can fly an airplane."

And that's not enough for me. I need at least two reasons to do something before I do it, preferably more. Funny enough, that doesn't apply to sitting on my ass and doing nothing. I don't need any reason to do that.

But I digress. Levels of failing. Something could be fatal, but so what? You could trip in your bathtub. Or you could fail by getting bored and giving up. That happens to me a lot, because squirrel. Or it could turn out that you're just no good at it, as is the case with me and musical instruments. None of these possibilities ever stopped me from trying something, though. One thing that does stop me is the amount of work involved for a certain level of reward. Brewing is like that. I have no interest in brewing my own beer, because a cursory examination of what is required told me that it's 1% enjoying the fruits of your labor, 2% actual brewing, and 98% cleaning. And yes, I'm aware that adds up to more than 100%.

Not worth it, not with thousands of breweries operating in the US alone, the products of which I could spend the rest of my life sampling with almost no effort on my part.

In other words, I have to believe that I'm going to enjoy the process, not just the end result.

Now, if I were assured that I couldn't fail at brewing -- meaning not only producing drinkable beer, but not getting bored with the process or finding out I have no talent for it after all -- I'd do it.

It's not flying, but it's close enough.

As I've mentioned before, I'm trying to see at least one movie a week at the cinema. Yesterday was the last chance for me to see Raya and the Last Dragon, so I opted for it over newer releases such as A Quiet Place Part II and Cruella, both of which I hope to see eventually but should be in the theater for the next few weeks. So hopefully I can continue to do brief reviews, because condensing a movie review into one sentence is as much a writing exercise for me as anything.

One-sentence movie review: Raya and the Last Dragon

This solidly-plotted, excellently-animated, and beautifully-voiced fantasy action movie from Disney succeeds in telling a compelling story; however, I question the appropriateness of the movie's central lesson (which seems to boil down to "trust your enemies;" a hell of a thing to teach a kid), and besides, I couldn't stop thinking that the movie's multi-pastel-colored dragons closely resemble My Little Ponies.

Rating: 4/5

6 Like • Comment • View 8 comments

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