Complex Numbers (Book)

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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/

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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:

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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 27, 2024 at 9:02am

#1079008

Revisited: "Stylish"

Almost four years ago, I wrote this entry in response to a 30DBC prompt: "Stylish"

The prompt was fairly long for a prompt, so the entry was fairly long for an entry. Prompt: "What is your blogging style? In your response, consider the following questions: What is your process of writing a blog entry - do you plan it out in advance, or just start writing? Who is your ideal reader? How did your unique blogging style emerge? Has your blog changed over time?"

Upon re-reading the entry, I was a bit disappointed that few of the answers would change between then and now. There's something to be said for consistency, but there's also something to be said for growth.

Yesterday, I made my habitual Monday foray to the local taphouse.

That's one thing that's changed. I still like that taphouse, but I don't go regularly anymore.

I sit outside, on their patio, because it's a better bet than dining indoors. There are no guarantees, of course, but the science points to a lower risk of Trump Mumps transmission if you're not inside.

This has changed, of course, because it's not 2020 anymore. As far as I know, I still haven't gotten Trump Mumps... but I've had a few bouts of cold-type illness, and never did bother getting tested.

None of which really has anything to do with the prompt, except to illustrate that I don't really plan out these entries, other than maybe giving them an hour or so of thought, usually while doing something else (in this case watching YouTube videos about science, philosophy, and the philosophy of science), and then, in the entry, I could write about almost anything.

My YouTube consumption has diminished since then, also. I despise ads, and they want to charge too much for no-ads. And even without ads, I got really weary of everyone telling me to "like and subscribe." Urging me to like, subscribe, comment, etc. is an absolutely certain way to ensure I never will.

I don't want to get tied down to any one subject, because so many things are interesting to me, and in the end, I'm not writing for any particular type of reader, but just to write.

That... wasn't exactly true then, and it's not exactly true now. It occurred to me several years ago that some of the best works of fiction were written, not with a particular demographic in mind, targeted to what market research suggests would be the most lucrative audience, but for an individual or small group of people. So, I imagine writing for one particular person. It's not always the same person. Still, it's not a lie; I don't write for a "type."

Thus, I really haven't tried to push myself into a "style." Sometimes I'm funny (or try to be; jury's still out), and sometimes I'm completely serious. Sometimes both at the same time. The problem there is I'm not sure anyone can tell the difference.

This bit hasn't changed.

When I started blogging, lo these many years ago, it was mostly about personal stuff, like the crap I started with today.

Clearly, I still do that when the situation warrants, like when I was traveling and had experiences to relate.

Obviously, I do still talk about personal shit sometimes, but I've arranged my life specifically to avoid drama, so very little happens to me that anyone else would consider interesting.

The downside of this is that when it does, I barely have the practice to handle it.

But writing isn't work. I suspect that if I ever made actual money from it, I'd probably start to consider it work and break out in hives.

Still true.

As I noted recently, I've managed to add an entry every day of this calendar year thus far, and I'm hoping to make it to December 31 (not that I'll stop then, but I do expect to take a couple of breaks next year).

Those breaks didn't happen, and I'm closing in on a five-year uninterrupted streak.

So, I guess, some things did change, but mostly things outside my control.

6 Like • Comment • View 1 comment

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