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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

about 7 hours 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

about 8 hours 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

about 8 hours 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

about 18 hours 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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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?

June 11, 2021 at 12:03am

#1011656

Useful

Just a little fun today.

The Forgotten Uses of 8 Everyday Objects

Some of the products we use daily have functions most of us are completely unaware of.

Yeah, like my mobile phone. Did you know you could use it as a phone?

1. THE TINY “EXTRA” POCKET ON YOUR JEANS

You’ve probably noticed that some of your jeans have a small pocket located in one of the front pockets. Many people think the tiny addition is meant to keep coins from jingling around in the larger pocket, but according to Levi’s, they created it to provide extra protection for pocket watches.

And no one has pocket watches anymore, except for truly eccentric attention-whores and, well, me, but mine's a family heirloom locked up somewhere safe.

Which means that jeans outlived pocket watches. There's something to be said about fashion that doesn't go out of style.

2. THE HOLE IN YOUR POT HANDLE

Most pots and many pans are designed with a small hole at the end of the handle. While they make for an easy way to hang your pots and pans when they're not in use, they were also designed with another purpose in mind: as a way to hold your spoon or spatula in place over the pot itself, and save yourself from making a mess of your stovetop.

Yeah, I've seen this idea floating around for a while. I call bullshit. I tried using the ones on my pans that way and ended up making a mess of my stovetop.

They are, however, indeed convenient for hanging the buggers.

3. THE LOOP ON THE BACK OF YOUR DRESS SHIRTS

If you look below the collar and between the shoulders on the back of many men’s dress shirts, you may spot a little loop. Though most men probably don’t use it for its intended purpose—at least, not often—it's there to provide a convenient way to hang up the shirt when a hanger is unavailable.

Whaaaa? That's what chairs are for. And as kids, we had rude names for these loops. "Fruit loop" was the least offensive of the bunch.

4. THE GLOVE COMPARTMENT

More like the user manual compartment.

5. THE HOLES IN YOUR BOX OF ALUMINUM FOIL

If you've ever studied a box of aluminum foil or cling wrap, you may have noticed that there are little indentations that, once pushed in, create small holes on either end of the box. Look a little closer and the reason for these holes is printed right on the box: "Press to lock roll."

I used to be one of those people who would read the fine print on anything, lest I miss something important. So yeah, I knew this. But when I try to use these tabs for their intended purpose, it's a bigger pain in the ass than if I don't.

6. THE DRAWER UNDER YOUR OVEN

If you keep cookie sheets, cupcake pans, and pancake griddles in that narrow little drawer under your oven, you’re in good company—so does most of the rest of the world.

Because that's what it's for and I refuse to revise my knowledge to fit any so-called "facts" about it.

7. THE ADDITIONAL HOLES ON YOUR CONVERSE SNEAKERS

They're talking about the air holes, but back when I had Converse sneakers, you know, when they cost like five bucks instead of 1500, I had all kinds of additional holes in them, none of which were intended by the manufacturer.

8. THE LOOP ON THE SIDE OF YOUR CARPENTER JEANS

THEY'RE CARPENTER JEANS WHAT THE HELL DO YOU THINK THAT'S FOR?

Also, did you notice that all of these are about holes? If I were a shrink, I'd have a field day with that.

Anyway, like I said, just a bit of fun, but I can't leave this without doing my quick review of Cruella, which I saw yesterday.

One-Sentence Movie Review: Cruella

I probably wouldn't have appreciated this movie as much if I hadn't spent the time, earlier this week, to watch both the original Dalmatians cartoon and its live-action remake; as it is, while my expectations were fairly low, it turned out to be a fun movie about the perils of working in the cutthroat fashion industry -- and maybe a few other, minor themes like betrayal and revenge -- consequently, as much as I desperately wanted to describe the movie as "spotty" to make a really, really bad Dalmatian pun, I cannot, because it's pretty tight, just like the outfits it features.

Rating: 4.5/5 (but probably more like 3.5 if you haven't seen or don't remember 101 Dalmatians)

8 Like • Comment • View 3 comments

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