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 1, 2020 at 12:17am

#984737

Monster

I thought I'd go ahead and kick off the month of June with an entry for "Journalistic Intentions"

[18+]

A bit of background if you can't be arsed to click on the above link: Long ago, Elisa: Middle Aged Stik

created a quote-remixing In&Out, which can be found here: "Fill in the Blank"

[18+]. Go ahead, give it a try; it's fun. The idea is to change a tired old clichéd sentence into something new, which is definitely an idea I can get behind. So for the June round of the blogging activity, she's selected fourteen altered clichés to choose from, submitted by our fellow members.

One of them was my own, so the least I can do is participate in the blog activity. So eight of my entries for the next five weeks will be inspired by these quotations. As usual, I'll be picking these at random as a personal challenge to see if I can come up with something interesting from anything, which has always been a kind of point of pride with me.

1. An over sized, monster truck on the highway with a competition sound system may not solve all your problems, but it will annoy enough people to make it worth the effort.
(Winheim Witheiw

)

You know, that sort of thing does annoy me, I'll admit it. But mostly just because anything loud that is not music annoys me. Dogs barking. Lawnmowers. Harleys. Leaf blowers. The trash truck on Tuesdays. Porn videos. But music is usually fine. Hell, if you're tooling down the road with your speakers cranked up to 11, and if I can hear the music over the blast of the face-melting sound system in my own Subaru, I might even like it.

Not so much the exhaust system.

But you know, I find there are two types of people in the world: people who think that there are two types of people in the world; and those of us who know better. Okay, no, seriously, there are at least two common reactions to the monster-truck-loud-on-the-highway scenario:

1. Meh, whatever. You do you.
2. There oughta be a law.

These two reactions typify pretty much everything. Someone's smoking a cigarette on their lawn. Someone's chewing their gum too loudly. Someone fails to put the shopping cart into the parking lot corral. Well, okay, I lean authoritarian on that last one. I mean, really, how fucking hard is it? I don't care if you have brats or you're in a hurry or both. You should have planned better. In both cases.

But if something isn't doing actual, immediate harm, I generally let it go. There's plenty enough drama in the world without adding to it by getting all complainey. So yeah, I lean toward #1 above. I know my rights, and one of them is most definitely not the right not to be annoyed.

I will say this, though, if you're one of the monster-truck-loud-stereo types, at least assuming you're a guy (which is a fair assumption if you're driving a loud monster truck):

I'm very sorry your penis is so small.

4 Like • Comment • View 2 comments

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