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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:

GeminiGem of House Lannister

45 minutes 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?

Lazy Writer est 4/24/2008

about 4 hours ago
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

Aennaytte: Free & Wild in GoT

about 4 hours 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.

Aennaytte: Free & Wild in GoT

about 4 hours 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.

Aennaytte: Free & Wild in GoT

about 5 hours 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 ...

Aennaytte: Free & Wild in GoT

about 5 hours 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?

Aennaytte: Free & Wild in GoT

about 5 hours ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

Robert Waltz

Apr 21, 2024 at 10:22am
In response to "Revisited: "Hack This""

🌕 HuntersMoon, ah, yes, my favorite words to hear (or read).

Also, that video is an excellent, if brief, explanation of the conundrum and how to resolve it.

1 Like

December 18, 2020 at 12:01am

#1000412

Tough Cookie

"30-Day Blogging Challenge ON HIATUS" [13+]:
18. Bake Cookies Day
As if we need a designated day for this, lol.
Write about your favorite cookie(s) or cookie baking experience.
Anything to do with cookies!

"JAFBG" [XGC]:
You wrote a Christmas list but accidentally addressed it to Satan instead of Santa. What gifts will you be getting this year?

Nothing either way because both characters are mythological.

But hey, I'm sometimes a fiction writer, so I can play along.

I would like the following things for Christmas:

A pony
Santa: I end up with a plastic Twilight Sparkle.
Satan: There's an ebony-maned steed with flaming red eyes snorting in my backyard.

A bike
Santa: A three-speed mountain bicycle.
Satan: 2020 Harley-Davidson Roadster waiting in front of my house.

A new gaming computer
Santa: Refurbished Dell
Satan: Acer Predator with liquid nitrogen cooled processor

A time machine
Santa: A digital watch
Satan: The TARDIS

A robot servant
Santa: Roomba
Satan: Data the android from Star Trek

On the downside, well, Santa would bring me all of those admittedly very nice things in exchange for some fresh-baked cookies (see, I worked the cookies into the entry too). I don't think Satan's interested in any cookies I could bake. Well... maybe if I made them double chocolate fudge chip with chocolate syrup drizzled on them... but no, I think I'd have to pony (pun intended) up something just a little more valuable.

Could be worth it, though, just for the Acer.

5 Like • Comment • View 5 comments

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