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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?

December 4, 2018 at 12:43am

#946804

Tea, Totally

I got hit by anxiety yesterday.

Historically, this isn't something that happens to me. I mean, sure, maybe if there's a specific thing generating it, like public speaking or having to go to a party where I don't know many people, I'll feel a bit nervous, or whatever you call it. But this is the first time I can remember just feeling it with no obvious reason.

I don't like it.

The only thing I can figure is after a long time, I'm finally feeling like being social again. I feel something other than a generalized sense of malaise and the certainty of impending doom. Those things, though, I've gotten used to. They comfort me. If this is what actual emotion feels like, then... no, thanks. I'd rather stay depressed.

Fortunately, there is beer.

This evening, BJ's (a chain brewery, but a decent one) had a Belgian Grand Cru style beer. It is delicious. I almost didn't go home.

But even I can't drink beer all the time. Mostly I imbibe Coke Zero; I want the caffeine but not the sugar/HFCS of regular sodas. And don't give me that "aspartame will kill you" crap; there are worse things out there.

Also, there's tea.

https://www.nbcnews.com/better/health/best-teas-energy-digestion-sleep-more-ncna...

Tea is the second most widely consumed beverage in the world (next to water), according to the Food and Agriculture Organization of the United Nations. While coffee drinking overshadows tea consumption in the United States, the Tea Association of the U.S.A. reports that 80 percent of American households have some form of tea in the cupboard, and more than 159 million Americans drink it on a daily basis.

I utterly despise coffee. Never got a taste for it. This, apparently, sets me apart from civilization in general. As an American, I'm supposed to be addicted to coffee. I think it's written into the Constitution or the Declaration of Independence: "We hold these truths to be self-evident, that coffee is the national beverage..."

But no, apparently I never got the memo. Can't abide the stuff. The smell gives me a headache, and being around people with coffee breath is probably the source of my antisocial tendencies. But that's okay, because once I tell people I don't drink coffee, they look at me like I'm a reptilian alien from Antares 7. It's like:

"I don't have kids."

"That's cool."

"I'm an atheist."

"Hey, I understand."

"I don't drink coffee."

"WHAT THE STEAMING PILE OF FUCK IS WRONG WITH YOU?"

So like I said, there's tea. "So why don't you just drink tea instead of that nasty cola?" Well, because for me, even the most highly caffeinated teas put me to sleep. I can drink a pot of black tea just before bedtime and sleep like a... well, not like a baby, because babies wake up every hour and a half which is why I never wanted one, so let's say sleep like a computer that's been powered down and unplugged.

If I drink it with breakfast, all I want to do is go back to sleep. It's nice when I want to relax, though. I can drink non-caffeinated herbal teas, but there's no freakin' point in drinking decaffeinated tea.

My favorite tea isn't on the list I linked above. It's harder to find in the US, but I've ordered it from Amazon. Its name is going to trigger your inner Beavis and Butthead, so let's just get that out of the way right now:

https://en.wikipedia.org/wiki/Pu%27er_tea

When you're done snickering like a 10 year old, I'll continue. Meanwhile, I'm going to go make me a pot of the stuff.

Ready?

Okay.

So yeah, Pu'er is strong, dark, earthy and bold. I drink it straight, or sometimes with just a bit of lemon because steeping it too long sometimes brings out a hint of bitterness. With a fairly high level of caffeine, it does what no other drink can do for me: make me relaxed and alert at the same time. It's a weird feeling.

And it sure beats the hell out of anxiety.

3 Like • Comment • View 9 comments

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