Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ January ► 2021
S	M	T	W	T	F	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Tuesday, Apr. 23, 2024

9:01pm EDT

Members: 946

Guests: 2,339

Total Online: 3,285

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

about 2 hours 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 6 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 6 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 6 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 6 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 6 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 6 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

January 24, 2021 at 12:02am

#1002690

Comoedia Maxima

PROMPT January 24th

Write about your most memorable or unique teacher from the years you were in school. What made them so interesting and what do you remember about them the most?

Well, I could talk about the science teacher I had in 8th grade who insisted -- and threatened me with the principal's office if I continued to contradict her -- that the reason Earth has gravity is because it rotates.

Look, I get it, not everyone can know everything. And if I'd heard that from an English or social studies teacher, I might have been able to write it off. But a science teacher? No wonder we're a nation of dumbshits.

But apart from that really quite abysmal gap in her knowledge, she was otherwise fairly forgettable.

So I'm going to go with my high school Latin teacher, Ms. P.

She wasn't my first Latin teacher. Freshman year, it was an older lady who'd been around the arena a time or two and brooked no shit from her students.

Second year, et cetera? New teacher. And by "new," I mean fresh out of ed-school.

I don't remember much Latin, but I do remember the scent of blood in the water.

Now, don't get me wrong; we all liked Ms. P. She was close enough to our ages to be somewhat relatable, but not so attractive as to be distracting to us boys. Gods, if we hadn't actually liked her, I can't even imagine the hell we would have put her through. As it was, it was mostly just harmless teenage pranks and antics.

Mostly.

Ms. P also taught math, but it was remedial math so, not to brag or anything, I wasn't in those classes. I mention this only because the math and science departments were clear on the other side of the school from the language classrooms. And, I guess, with her being a new teacher, the evil genius who did the scheduling put her math period immediately before my Latin class that first year she taught.

This gave us plenty of time to hone our comedy skills before she showed up.

At the end of a day, she'd put an English vocabulary word on the blackboard for us to ponder prior to her arrival the following day. (Why English? Well, in case you haven't noticed, over half of the words in English have Latin roots; the only reason it's considered a Germanic language is the sentence structure. So the vocabulary word was, I suppose, an effort to provide a reason why learning Latin is relevant.) So we did ponder the word - usually by writing a sentence wherein that word was used as a pun, and/or by providing a punny definition. Example: "Bacteria." "The rear part of a cafeteria."

Yes, I know "bacteria" was from ancient Greek, not ancient Latin, but it's the only one I could remember after all these years. Don't be pedantic.

Then there was Rufus Roman.

Rufus Roman was a stick figure with one of those brush-top helmets you see in movies about ancient Rome, and he held a gladius and a scutum.(sword and shield). We always drew him, on the blackboard, with either a big smile on his face, or, sometimes, with an expression of abject terror (when facing his archenemy, Barney Barbarian.) (Barney, of course, wore a helmet with horns, and an axe, and sported a beard and a mean, toothy, growly face.)

This was, and still is, the entire range of my so-called artistic talent. It never developed further. Fortunately, my comedic talents did. Well. Sort of. Maybe. You can decide that for yourself, and keep it to yourself.

Anyway, we could all tell that Ms. P. was trying very, very hard to maintain discipline in class by not acknowledging the comedy gold mine she'd walk into every time she'd march over from the other side of the school and look at the board. But she didn't succeed. Sometimes she even laughed out loud before she composed herself and very pointedly erased our masterworks.

One day, I think maybe it was because she'd forgotten to post the vocabulary word, we spent the five minutes we had before the teacher walked in by turning every piece of furniture in the room 180 degrees. As I recall, this involved a couple of filing cabinets, all of the student desk/chairs, the teacher's desk and wheeled chair, a lectern, and probably a few other odds and ends. There were like 8 of us in the class so it didn't take very long. And when she came in, at first she didn't notice.

Now, it's important to note two things: One, every day, she'd come in, sit down, stretch her arms to the sides of her desk, and wheel herself forward so her legs were under the desk. And two, the desk itself had a barrier on the student side. Well, so after everything got turned around, she simply swiveled the chair around, sat down, grabbed the desk, pulled herself forward and BANG her knees hit the wall on the front of the desk.

Fortunately for us, Ms. P. had a decent sense of humor and a high tolerance for pain -- both necessary qualities for a high school teacher to have.

She'd be in her 60s now, I guess. If she's still teaching, I bet she no longer brooks any shit whatsoever from her students.

We taught her well.

4 Like • Comment • View 8 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/1-24-2021

Site Links:

Resources:

Need help?

Please post questions in
our support forum.

Places of Interest: Unique Wedding Invitations for unique wedding needs. Color Copiers found here.
Baby Names can be hard to pick. Hands-free hygenic toilet seats covers. Dramatic Music rocks.
Vampires are people too. Write Poetry here. Try this Stock Market quiz.
Teaching is a noble job. Get info on Tax Refunds.

All Writing.Com images are copyrighted and may not be copied / modified in any way.
All other brand names & trademarks are owned by their respective companies.

Generated in 0.73 seconds at 9:01pm on Apr 23, 2024 via server web1.