Complex Numbers (Book)

Blog Calendar

◄ September ►
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
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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:

tj-Merry Mischief Maker

about 8 hours ago
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

a day ago
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

a day ago
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

a day ago
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

Access Restricted

This is a private area. Access has been restricted and you may not view it under its current settings. If you feel you should have access, please contact the area's owner and request access.

Note: To contact a member via email, click the small envelope icon to the right of their handle. You must be logged into your account to send an email.

2 Like

Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

September 23, 2024 at 4:10am

#1077168

Bière Snob

Yesterday morning got off to an auspicious start as the really quite obnoxiously loud building alarm went off.

Naturally, being American, I sat down to write an official letter of complaint to management, and prepared to give the hotel 1 star reviews on Yelp, Google, and Tripadvisor. How DARE they inconvenience a US citizen?

...yes, I'm kidding. Duh. I took long enough to put pants on, which may not have been the wisest course of action for myself, but you know me, always thinking of others' comfort. And then I proceeded down five flights of narrow, steep, half-spiral stairs that are probably older than my entire country.

I'd been awake, though not for long, when the alarm went off (hence the pantsless state, as I was only beginning to get ready to go to the hotel breakfast), so at least I didn't have another heart attack from waking up to that. But on my way down, I got to wondering whether my travel insurance would cover the loss of all my shit from the hotel burning down. Probably not, I reasoned, because insurance only covers whatever doesn't happen to you.

On the descent, I was joined by other people who also had the good sense not to use the elevator during a fire alarm (one of whom had stopped to pack his bag), and we all spilled out into the lobby, where a receptionist explained to us, in perfectly good English, that someone had made smoke in the breakfast kitchen and it wasn't actually a fire threat.

My fellow travelers grumbled and started marching back up the stairs (the elevator is one of those tiny European ones with the manual outer doors, obviously retrofitted at some point after electricity was invented), but I followed my original plan and slipped down to breakfast, where I specifically asked for le petit déjeuner bien cuit, or breakfast well done (in the sense of a well-done steak). Because I am, after all, an asshole, but at least I'm a funny asshole.

The travel agent's plans for me yesterday were: Eiffel Tower, Arc de Triomphe, Champs "Ulysses" [sic], and the Seine. But none of them involved tourist reservations; those were just their suggestions for famous shit to do while in Paris.

So, instead, I did what I always do in a new-to-me city: I found breweries.

You don't think of beer when you think of France, and generally for good reason. There are a few decent large-scale breweries in the east, adjacent to Belgium and Germany so that those countries' skill in brewing manages to spill over the border. But for the most part, French beer is, historically, liquid ass.

But, like the Anglophone countries I'm used to, France has developed a craft beer scene. I only had time to visit three of them, but my overall impression is: just like the aforementioned Anglophone countries, some of the beer is excellent, and some is... well... less than excellent.

I'd never know that, though, if I didn't try. I'm pretty sure I've said this before in here, but I enjoy tasting all beer, even the bad stuff, because, as the great philosopher said: "If everything was cool, and nothing sucked, how would we know what was cool?" (I can't remember if that was Beavis or Butt-Head.)

Now, when I say "tasting," I don't mean I got pints (or, you know, 500ml, close enough) of each one, but did the small-serving flight thing. So no, I wasn't utterly wasted when I was done. But I had achieved beerenity, which has been elusive to me lately. I might have actually smiled as I walked back to the hotel, across the Seine, and through the courtyard of the Louvre, where I paused to snap what is surely the most French photograph I could possibly shoot.

7 Like • Comment • View 1 comment

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