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:

Write_Mikey_Write!

about 10 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 12 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

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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