Complex Numbers (Book)

Blog Calendar

◄ October ►
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

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 20 hours 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

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

October 6, 2024 at 4:59am

#1077831

Like a Bosteels

One thing I insisted upon during trip planning was to visit Brouwerij Bosteels.

This is an ancient brewery which creates two of my favorite Belgian beers: Tripel Karmeliet and Pauwel Kwak. (The link there goes to the English website.)

The difficulty: the brewery is located in a small village called Buggenhout, kind of between Brussels and Antwerp. And I'm still in Bruges, to the northwest. Yes, Belgium is a relatively small country, but it's not that small (about the size of Maryland, though more compact), so trains were involved.

This meant that I had to walk the mile (roughly 1600 meters) from the hotel back to the train station and, yes, my nemeses the cobblestones were heavily involved, though at least I wasn't rolling luggage. From there, I caught a train directly to Ghent (or Gent), then switched trains at a heavily-under-construction station to a stoptrein (which I gather is the equivalent of a "local" in the US) going through Buggenhout. All while being mostly unable to read signs or understand announcements.

While this is part of the adventure of traveling, I was on a schedule; I had to be at the brewery by 1:00pm (or 13:00 in the superior Euro style).

I managed. But then I had to walk again, this time about half a kilometer, to the gigantic brewery, and here, Google failed me in a way that signs in Dutch did not, giving me the wrong location of the entrance. As the brewery is, as I noted, gigantic, this meant walking around an enormous block to find the tour location and, yes, there was a preponderance of cobblestones.

I found it, albeit a few minutes late, but they let me in anyway. After a quick taste of a beer, the guide (who resembled Mirror Universe Jean-Luc Picard, in that he was bald but had a goatee) took us around the brewery operations, which, it being Saturday, weren't active at the time. This is a good thing, because we didn't get in anyone's way and I could actually hear the guide because the machines weren't operating. Point is, you know the Wonka movie? Yeah, that was me gawking at this enormous brewing operation.

Now, my appreciation for Bosteels wavered a bit a few years ago, when AB/InBev bought them. (AB/InBev is an enormous Belgian company, but it's best known for its first initials, which stand for Anheuser-Busch.) But they didn't change the beer in any noticeable way. I'd hoped, because of the big corporation's greater reach and distribution network, that this meant we would be getting more Kwak in the US, but I still can only rarely find it in Virginia. I see Tripel Karmeliet quite often, though, so that's okay.

Interesting thing about Kwak. Each Belgian beer has its own dedicated glassware for serving; this is one of the delightful aspects of Belgian beer. Most of them are variations on a theme, though; something resembling a goblet or Holy Grail, or perhaps a pilsner glass, or, you know, another kind of glass you'd expect to find beer in. Kwak glassware is unique, resembling instead a test tube on a wooden stand. Today's photograph, below, is of a serving of Kwak, so you can see what I'm talking about. I possess two such glasses back home, because on those rare occasions that I do find the beer near me, it's imperative that I use the proper receptacle, and there are two of them because, sometimes, I share with friends.

The funny thing is that a bartender here told me that the glassware, being so different, tends to get stolen from bars. So the bars here, he said, require that you put up one of your shoes as collateral to ensure they get the glass and stand back when it's empty.

This would definitely be a deterrent for me because, well... cobblestones.

I didn't have to get one of my shoes taken hostage at this brewery, but they did let me have a Kwak, and yes, it is much better to drink it at the source.

Between the opening beer, a serving of Tripel Karmeliet, and the Kwak, I was pretty far gone by the time the tour/tasting ended (I'm no lightweight, but Belgian beer tends to be high-octane), and I had to retrace my steps, and the trains, back to the hotel. Easier said than done, because I was still kind of out of it when I got off at Bruges, and had to walk the mile back to the hotel. Along the way, I gave up and had dinner (and a beer) at one of the many sidewalk bars in the old town.

All of which is to say: Mission Accomplished. I only have a few days left here, and rumor has it there's a hurricane (yes, a hurricane, though "only" of tropical storm intensity) coming, but I've now done what I most wanted to do.

As promised, a picture of how Pauwel Kwak is served (bonus: Mirror Universe Picard):

5 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.