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:

Wordsmitty ✍️

about 11 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 14 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

about 16 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

Lilli Munster 🧿 ☕ 🎃

Sep 24, 2024 at 9:10am
In response to "All Out of Louvre"

Have a wonderful time in France. Have you run into Annette in France yet? She's there too!

2 Like

June 21, 2020 at 12:10am

#986107

Business

Entry #6 for "Journalistic Intentions"

[18+]

3. That's always an interesting concept when you try to mind your own fucking business then you end up on face book or twitter.
plainsue

So, again, no idea what the original quote was, and it probably doesn't matter.

If you've been following along, you already know I'm no fan of social media. This site here is about the closest thing I ever use to social media, because it's relevant to my interests and most of us at least try to be kind to each other, or, at least, not hateful. There are exceptions, of course, and being a mod probably skews my viewpoint, but by and large I've had much better interactions here than on Facebook.

I haven't used my Facebook account in years. Every time I think, "I should close that account," I realize I have no idea what the password is. And then to recover the password, it makes me identify friends from their pictures.

Difficulty #1: Most of my Facebook friends are from this site, and I haven't met most of them in person.

Difficulty #2: I have mild face-blindness, so I can't identify faces even of people I know most of the time.

So, yeah, if you've tried to get in touch with me on Facebook, or friend me there, I'm not ignoring you. I just can't log in or close my account.

Apparently, Facebook is forever.

Twutter's another story. I first heard of it, I don't know, sometime back in the noughties before it became the Official Platform of the Pronouncements of the Most Powerful Person in the World. The way I first heard of it, a friend of my then-wife was talking about it. She's an engineer with a rather earthy sense of humor, and she described with some glee how a fellow engineer had rigged his office chair to Twit every time he farted.

As far as I've been able to determine, that site hasn't improved any since then, and may have even gone downhill. Considering that I think fart jokes are the lowest form of humor, that's really quite a feat.

So, no, I don't have a Twatter account and never have. The occasional really interesting thing from it always gets posted elsewhere, so I really don't feel like I'm missing anything.

And don't even get me started on the cesspool that is Instagram. Fortunately, that's not part of the quote above, though as it's owned by Facebook, it's relevant to mention it.

Oddly enough, I've made a shit-ton of money from Facebook. But that's another story entirely.

I've heard people say that the internet is not reality. I don't think that's the case. I was an early adopter, back in the nineties before everything turned commercial, and even then it was an extension of reality. I've met people from all over the world, first online and then in person. Some of my closest friends became so on this site, before I ever met them in person. To say that it's not "real" is to dismiss the people on the other end of the network as non-people, and I think it's dangerous to label anyone as a non-person. That never ends well.

So I understand the draw of social media. I just don't participate. I'd rather mind my own business, and if some picture of me ends up on social media, well, I just shrug and go on with life. But then, I haven't done anything egregious enough to get doxxed or called out. If I did, though, it's probably a sign that I'm not actually minding my own business.

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