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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

Apr 24, 2024 at 4:26pm
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?

September 1, 2019 at 12:46am

#965323

Nineteen

PROMPT September 1st

Celebrate 19 years of Writing.Com by writing a thank you letter to someone on WDC or a thank you letter to the website itself. Then, visit "Writing.Com Party Central 2023!"

(the item will be locked until the wee morning hours of Sept 1st) and tell us what Birthday-related fun you are most excited for.

What do you want me to do, get mushy? I don't do mushy.

But let's give this "thank you" thing a shot.

Dear The StoryMaster

and The StoryMistress

:

19 years, huh? Funny, it only feels like 15. Oh, that's right, I've "only" been here for 15 of those years. Sometimes I still feel like a newbie, but that's because there's so much to do here I still haven't exhausted all the possibilities - a testament to all the good work you've put in to keep things interesting.

19 years is, as you know, a long time in cyberspace. I can't think of too many websites that have been around, without fundamental changes, for longer than that. True, my Amazon account is older, but when I signed my life over to Bezos, it was still "Earth's Biggest Bookstore." The streaming video that sucks away even more of what could be writing time didn't come until later.

A noteworthy accomplishment. But there's more.

See, I've been noodling around on the internet for a long time, way longer than 19 years, and it can be a real shithole. Trolls, scammers, assholes, racists... people who are there to tear you down, pounce on your inadequacies, splatter you with sewage.

But not here. At least not for very long. And that's remarkable.

You've created a community that, for the most part, works. Sure, there's friction - can't avoid that - and it's impossible to please everyone, but you have, for the most part, built a network of relationships based on mutual courtesy and respect.

Because of Writing.Com, I feel like I've grown: as a writer and as a person. More than that, though, I've made friends here - lifetime friends. I've traveled to places I might never have otherwise seen, met people from all over the world both online and in person, had pleasant conversations with people very different from me. This has been my cyberhome for a few days shy of 15 years, and even when I don't write, rare is the day that I don't at least visit, check in, see what's going on.

I'm glad to be here; I'm proud to support the site; I'm honored to be a part of this community.

So.

Simply:

Thank you.

Okay, enough of that.

On to the next part of today's mission. I'll just click on the Party Central link and...

Holy forking shotballs! That's a lot of stuff. Looks like there's something there for everyone.

But one activity stands out for me. See, when I first got here 15 years ago, most of what I stuffed into my port was written for one contest. It's been around longer than I have, obviously, and I have the honor of being involved with it to this day - as a judge, but also sometimes as a contestant as well. In addition to the "contest" aspect, it's just a terrific writing exercise. Yes, of course I am talking about

FORUM

The Writer's Cramp

(13+)
Write the best story or poem in 24 hours or less and win 10K GPs!
#333655 by Sophy

So that's what I'm most excited about, if only because I'm a part of it. But I'll be checking out other things as well.

5 Like • Comment • View 5 comments

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