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:

Turkey DrumStik

about 12 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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').

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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

September 16, 2018 at 1:23am

#941506

Pure Imagination

The first movie I recall seeing in theaters was Willy Wonka and the Chocolate Factory.

It's possible my parents took me to other movies before that. I don't remember, and I never asked them. But that one stuck in my mind, mostly because of the tunnel scene - that sort of thing clamps onto you when you're five years old. It's entirely possible that my entire psychological complex has its roots in that one scene. I was pumped when Thor:Ragnarok paid it homage.

Anyway, that never stopped Adult Me from liking the movie, after the usual teenage "that's kid stuff" crap. Even as a kid, I thought the moral lessons were a bit over the top, but there's enough depth to the movie as a whole for it to be worth revisiting. Plus, Gene Wilder was always awesome.

So my local theater - an Alamo Drafthouse, which if you're lucky enough to be in one of their markets you know what I'm talking about - is having a Wonka screening this Friday, complete with a couple of the actors from the movie showing up for a Q&A afterwards (the former kid actors, of course - pretty sure all the adults have gone to the great chocolate factory in the sky).

For the uninitiated, Alamo Drafthouse is just that - a drafthouse and a movie theater. It's adult-oriented (not in a tawdry way) and the theaters aren't usually stuffed with screaming kids, so watching something like, say, Incredibles 2 can be a pleasant experience. This particular screening allows kids 6 and up, which I find amusing because like I said, I was five when I first saw it in the theater.

Of course I'm going. Wouldn't miss the opportunity to get completely drunk and then watch the tunnel scene. Oh, sure, I could do it at home; I have it on DVD. But there's something to be said for watching it in a room full of other fans, on a big screen.

Now, let's get this out of the way: I never can bring up a movie that's been remade without someone commenting on the remake. I say Willy Wonka; they bring up Johnny Depp. I say Ghostbusters; they have to ask me if I liked Ghostbreasters . I mention the classic Total Recall, and someone has to mention the absolute crap remake of it. Point is, stop it. I get that they have to remake movies because money. Some of them are good. Some of them suck. But when I talk about Willy Wonka and the Chocolate Factory, I do not want to hear about Charlie and the Chocolate Factory. If I wanted to talk about the remake, I'd talk about the remake. So if that means I have to bring it up to forestall discussion of it, so be it.

3 Like • Comment • View 3 comments

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