Complex Numbers (Book)

Blog Calendar

◄ June ►
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:

Wordsmitty ✍️

about 2 hours ago
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

1 Like

🌖 HuntersMoon

about 5 hours ago
In response to "Gray Matters"

I've always believed "better gray than gone away..."

1 Like

tj-Merry Mischief Maker

about 24 hours ago
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

a day 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

Dec 23, 2024 at 4:55pm
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🎁

Dec 23, 2024 at 12:56pm
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

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
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

June 29, 2024 at 10:51am

#1073318

Je Voyagerai

I thought I'd provide a travel plan update today, after discussing my general idea here a week ago: "Discomfort Zone"

On Monday, I looked at nearby travel agents. Just their websites and Google reviews.

I'm an avid Google reviewer myself, mostly of breweries (writing ability does have some practical use), so I know to take any review with a grain of salt, much like the item reviews here: each is (usually) just one person's opinion and experience, and everyone, reviewer and reviewee alike, has their good days and bad days. Also, one needs to be aware that some 1- and 2-star reviews are competitors trying to steer people away, while some 4- and 5-star reviews are salted by the company itself.

Still, it can be helpful to take a look at reviews all across the spectrum. If there are enough of them, you can be pretty sure there are some genuine experiences in there.

Anyway, one travel agent specifically bills itself as "luxury travel." I'm not elitist enough for that. Another had mediocre reviews at best. I settled on someone who's been active in town for almost as long as I've been here.

Tuesday, I drifted on over there to try to get a feel for what to expect. Sure, I could have called, but it's not far away.

Now, I know some people scoff at the idea of going with a travel agent. Why not just go and experience stuff? Make your own travel plans, your own schedule? Normally, I'd agree. But then I realized: part of the reason I travel is to experience stuff I haven't experienced before. And I've never used a travel agent, so why not experience that for the first time? Besides, I'm entirely too lazy to work out lodging and transportation details myself for a trip to an unfamiliar place.

They gave me a really good idea as to what to expect in terms of process and fees, and promised to get back to me.

On Wednesday, they sent me a few emails, but I had to visit the dentist to get some drilling and crown work done. That shot my whole afternoon (and most of my medical budget), and also the next day while I dealt with the soreness.

Still, I found the energy on Thursday to take a look at the emails, and immediately questioned my decisions when I saw what-all would be required. Passport stuff. Credit card info. Read these T&Cs. Sign here. Sign there. Initials everywhere. (I'm going on a trip, not buying a fucking house.) What kind of trip? What sort of lodging amenities do you want? What's your budget?

"Your vacation is an investment..."

No. No, it is not. An investment is something that's expected to increase in value over time (whether it actually does or not is another issue). Stocks can be investments. A house can be an investment. A car is not, unless we're talking about the classics. A vacation (or, in my case, a voyage, since retirement means permanent vacation to me) is purely spending; the only returns I expect are experiential and emotional.

Words mean things, you know.

On Friday, I called the contact person I'd spoken to and who'd sent me the emails, and she (her name is, amusingly, Karen, and she's a manager, having become the very thing she swore to destroy) assured me that most of these things can be worked out when I meet with the actual travel agent a week from Wednesday.

However, I have no idea what to expect for "budget."

When road-tripping here in the US, I have a pretty good handle on it: I know, to a fair degree of accuracy, what I can expect to spend on gas, food, and lodging each day, and maybe throw in a little extra to try beers at breweries. I'm also not entirely ignorant of what airfare costs, though that varies wildly depending on season and how much discomfort I'm willing to put up with (not a lot, at my age).

I don't want to cheap out, because contrary to popular belief, money does, in fact, buy happiness. Or, well, at least it buys comfort and booze, which is close enough. I also don't want to spend my life savings; I kind of need that for, well, life. Somewhere in the middle would be nice.

What's important to me is that I get value for my money. Like, not spending $100 (or the equivalent in euros) for something that's worth $50.

I figure maybe I can explain that to the agent when I meet with her, and we can work out the details from there. Budget will, of course, help to determine how long the trip lasts and how many different places I can go to. And right now, I'm flexible on those things, as well as on actual dates of travel (I'm hoping for this fall, because I'm definitely not going in the winter, which means if it's not this fall it'll be next spring, and I just don't want to wait that long).

In conclusion, I'm definitely doing this (barring, of course, emergencies). I just don't know any of the details, yet.

4 Like • Comment • View 2 comments

© 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.