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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 13 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 13 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 14 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

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

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

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 2, 2019 at 12:28am

#965382

Waltzing towards Bethlehem

PROMPT September 2nd

As you may or may not be aware, in the early days of Writing.Com, SM and SMs hosted in-person Conventions for members! From everything I’ve heard from the site’s veteran members, these get-togethers were beyond memorable and so inspirational. Take a trip to the past by reading this item advertising the 2006 WDC Convention: "Writing.Com Convention 2006"

. Then, share your thoughts on what a Convention hosted today might look like. Where would it be hosted? How many members could attend? What activities would take place? Who would you want to meet in person? Have fun!

Oh, man... that's a blast from the past.

I just went over the 30DBC participants list this month, and realized that, if memory serves (and, increasingly, it doesn't) I'm the only one of us who was there.

That's right - I attended the 2006 Writing.Com Convention. In some ways, it seems so long ago; in others, it feels like just last month.

I was, if you can believe it, the newest member at the Convention. I even got an actual plaque confirming that. I still have it, displayed in my home office. At the time, I was a Preferred Author; I can't remember exactly when I got my blue suitcase, but it was shortly thereafter.

But you'll forgive me, I hope, if I don't visit the given link. I am, as you know if you've been following along, prone to depression - less so, these days, but still, a trip down memory lane involves tiptoeing through a minefield.

If you're interested, however, I still have my convention recap. The story is loaded with links to other author portfolios, some of which, sadly, are broken now, as some of the members are no longer with us. The title, by the way (which I blatantly stole from my younger self for the title of this entry), is a reference to the Convention's location in Bethlehem, PA, near WDC World Headquarters (aka The StoryMaster's basement).

I solemnly swear that every word in this is true.

Waltzing towards Bethlehem

(18+)
And what rough beast, its hour come round at last, Waltzes towards Bethlehem to be born?
#1135858 by Robert Waltz

There was a recap contest, and that item took second place. But since the first-place winning entry is no longer available, what you have there is, objectively, the best recap of the 2006 Writing.Com Convention that you will ever lay eyes on. If that doesn't fill you with existential dread, nothing will.

As for a Convention today... well, one can only dream. PA is a nice place, and Bethlehem is certainly convenient for Staff, but I feel like it could be better-attended if it were near a major hub. For selfish reasons, I'd pick DC or the New York area. At one point, Staff tried to host a mini-convention in Newark, but sadly, that turned out to be a bust - except that I got to spend the day with two of my good friends: one who got me to sign up here in the first place, and another whom I met at the 2006 Convention. We went to a comedy club, and we drank quite a bit.

In terms of what activities I'd like to see, well, drinking of course. Okay, maybe the prompt meant official activities. All I can say there is what worked in 2006 could still work today: writing workshops, naturally; Open Mic Night; a disco (hey, maybe we could combine the two and have some karaoke - wait, where are you all going? Come back!); auction; etc.

There have been so many new people joining us since 2006. I've met a few, but would love to meet everyone else.

Just... no zombies this time, okay? Deal? Deal.

6 Like • Comment • View 7 comments

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