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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 19, 2021 at 12:13am

#1010404

Adventure

You know what else it's wonderful to get back to doing?

I'm sure you know what I'm about to say. Yep, you've got me completely figured out. But I'm going to say it anyway.

Brewery visits.

Yesterday a friend and I visited two local breweries that, somehow, neither of us had ever set foot in before, and they were around in the Before Time so I have no excuse.

As is my usual procedure in such cases, I got a tasting flight of a variety of different beers. And with one exception, they were all really damn excellent beers (the one exception was just a really excellent beer).

Now, I don't want to give anyone the impression that I like all beer. I do not. For example, and I'm sure I mentioned this in here before but what the hell, I was presented with a lime-salt lager a few weeks ago that was utterly foul. But all that does is make me appreciate the good stuff that much more.

Still, not only did I like the beer, but now I'm going to have to go traveling again just so I can find more new-to-me breweries to try. I'm out of local options. Though that doesn't preclude me going back to those.

Edit:

PROMPT May 19th

Write about the most historic world events of your lifetime. How are they (or will they be) remembered? What will the history books focus on?

I know I've written about it before, but during my lifetime, the one historic even that stands out as the "most" is the first moon landing in 1969.

Certainly there have been other important events, and will be in the future, but in my view, the landing of humans and their technology on a separate world for the first time is not only the most significant thing we've ever accomplished, but possibly the most significant thing we can ever accomplish. Oh, sure, maybe we'll plant feet on Mars or soar through interstellar space, but there can only have been one "first time."

Of course, the way history books are trending, they won't see it that way. Possibly they already don't. No, instead of acknowledging this amazing feat of science, technology, teamwork, courage, curiosity, and sheer human determination, they'll probably spin it as:

- It wasted resources that could have better been used for other pursuits (it didn't).
- The effort wasn't inclusive/diverse enough (fair, but irrelevant).
- It was a vast international dick-measuring competition (also fair but irrelevant, as the competition produced results).

Worst of all, though, are the ignorant cockwads who deny that it ever happened at all, that it was a huge hoax. I'm not even going to bother to try to go into the reasons why they're wrong, and I fully admit that at this point some of them are just trolling for attention, same as many flat-Earthers. But I will mention why it's utterly maddening: because to deny that we managed to put a human on the moon not only denies the significance and importance of the accomplishment, but also denies human achievement itself. Denying it is also tantamount to saying: "we are human and thus incapable of great things," so it also denies something basic about our nature and what we are capable of.

Well, I've banged on enough.

I will say, though, that a close second to the moon landing in terms of historical events of great significance was the day in 1978 when Jimmy Carter signed legislation permitting home brewing, which eventually led to a proliferation of commercial craft breweries.

But I fully admit that this one may just be my personal opinion.

4 Like • Comment • View 5 comments

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