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 22, 2020 at 12:29am

#986175

The Candyman Can

I'm still working on this week's Comedy newsletter. Sometimes they come to me easily, like last month's, which I'm particularly proud of. But I think I shot my wad on that one, because this week I'm pretty much stumped.

And it's not like I can go to other comedy writers for inspiration. I'd just end up stealing their bits, without even knowing I've done it, because my memory is crap. Hell, I've stolen from my own older newsletters before, without realizing it. That's an occupational hazard, though, when you've been at it for...

(math)

Thirteen years?!

It doesn't help that I try to inject humor into almost every blog entry, and that I've been doing one of those pretty much every day. The joke tank goes empty after a while. I've cheated in the past and adapted one to the other, but I just wasn't feeling it this time.

So today I'm going to link a comedy article that also touches on some of my favorite other subjects: movies, folklore, and the sometimes invisible line between reality and fiction. And also ragging on Indiana. I was born there, but my parents had the good sense to flee the state before I was even two days old.

And hell, I'll even make this one another Merit Badge winning mini-contest opportunity.

https://www.cracked.com/article_27320_when-i-was-growing-up-in-indiana-candyman-...

When I Was Growing Up In Indiana, Candyman Was Very Real

You might be aware that soon there's going to be a new Candyman movie coming out, co-written by Get Out's Jordan Peele, and honestly, I'm not even that mad that one of Hollywood's most exciting new voices is rehashing old properties. Because Candyman is something that, as far as I can tell, is unique in all of cinema: a fictional film whose central thesis can be demonstrably proven, and if that's too Film School for you, let me put it this way -- Candyman came true.

Oh, great. I barely know who Jordan Peele is, and I've never even heard of Candyman (probably because, again, my parents swept me out of Indiana before I could even gurgle).

My relationship to the horror genre is similar to my relationship with jazz: I find the vast majority of it boring, but the stuff that I do like I really like.

Ah. Yes. I can relate.

See, I witnessed a double homicide with a shotgun before I was old enough to drink, so horror gore's as unshocking to me as finding a raw hogsnout in my Moons Over My Hammy.

Okay, no, I can't.

Which brings me to one of my favorite horror films: Candyman. First of all, Candyman is based on a (very different) short story by Clive Barker, an author I admire so much I have a signed photograph of him sitting on the desk I'm writing this article on.

When I was going through a horror phase, I read a bunch of Clive Barker. I don't remember if I read that one or not. I'm certain I've never seen the movie this writer is talking about. But if nothing else, click on the article above, scroll down to the bit I just quoted, and then take a good look at the photo just below that text. Visual comedy can be hilarious, and it's one thing I can't do as much of here as I'd like.

Maybe if I were actually funny, I could write for Cracked.

One of the central themes about Candyman is that whether or not a story is "true" is irrelevant -- if enough people believe in something, the end result is more or less the same whether the thing is real or not. It's why we still have the TSA even though in a test conducted by the Department of Homeland Security, the TSA failed to confiscate weapons snuck on board 67 out of 70 times, a failure rate of 95% -- the TSA is roughly as effective as fishnet condoms.

I've been saying something like this for years. You get something that enough people believe in, and the result is the same. George Washington chopping down the cherry tree? Probably never happened; doesn't matter. Ben Franklin with the whole lightning kite thing? May or may not have happened; doesn't matter. Paul Bunyan? Certainly didn't exist as advertised; doesn't matter.

I'm going somewhere with this, I swear. So Candyman is about a semiotics student researching urban legends for her thesis.

Any movie that features a semiotics student is definitely one I should see.

According to my goddaughter in Indiana, kids are still scaring each other with stories about Candyman just as much as they are with stories of Slenderman. Candyman has woven himself into the mythology of the Region, and I can personally assure you the fear he engenders is very, very real.

The way these things usually work, we don't know how myths like these get started. Lately, though, new ones have cropped up, like the above, and we do have some idea of their origins. And like this author notes, in the end, it's hard to tell myth from reality sometimes, because the myth has real effects. Like how you're so sure there's a monster under the bed that you spend the rest of your life making sure your toes are always covered by the blankets because blankets are an anti-monster-teeth force field (one that, somehow, doesn't work on cats).

So here's today's Mini-Contest: In the comments below (not in the newsfeed, please), tell me about an urban legend you know. Or one you just came up with; who knows, maybe we can start our own mythology here. It doesn't have to be long or involved, just the name and the scary part. Mothman, Jersey Devil, Justin Bieber, whatever. But you can explain as much as you like. I'll pick the one I like best and the author gets a Merit Badge tomorrow (probably a Horror/Scary one, but whatever I think is appropriate). As always, you have until the Witching Hour...

5 Like • Comment • View 8 comments

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