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 21 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 23 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.

January 14, 2020 at 12:02am

#973347

You Can't Count On Me

PROMPT January 14th

Write about a time when you made a wrong assumption. Did you realize your mistake right away, or did someone tell you later? What did you learn from your mistake?

Me? Make assumptions? Mistakes? What?!

Oh, fine, here's one.

Generally, I like to buy non-consumables exactly once. It saves money, which can better be used to buy beer and scotch. It really annoys me when something wears out and I have to buy a replacement; it's never the same and I'm out of sorts for weeks afterward because my routine has been threatened. The only exceptions are things like computers, which I'm aware have to be replaced every few years, if only to keep up with the latest gaming technology.

As a result, I never have anything to sell or to donate to Goodwill or whatever; by the time I'm done with something, it's hopeless.

I'm just explaining this because it's important to know my mindset going into these things.

So. Back when I was married, my wife brought home a new shower curtain. Okay, fine, even I could see that the old one had outlived its usefulness and was at that point of interest only to the most dedicated biology post-grads. But, determined to make this one last longer, I picked up one of those spray bottles of chemicals that, supposedly, when sprayed onto shower surfaces after a shower, help to keep it clean.

One day she caught me spraying the curtain with the tilex or whatever it's called. (Hey, we were married; shut up.) "Why are you doing that?"

"To make the curtain last longer."

"Don't bother with that. We'll just get another new curtain."

I ignored her and did it anyway. I'm not buying another damn shower curtain. Those things cost money!

It was only some years later, we'd separated for reasons that probably were unrelated to that argument, that, while in the shower and thinking "maybe it's time to get a new shower curtain; this one needs to go to the Institute for Xenobiology," that it hit me.

A shower curtain is like $12.

A bottle of that spray shit is like $5.

Even assuming that I spend half the spray shit, usefully, on long-lasting surfaces like tiles, it would take about five sprayers to break even. It would be cheaper to buy a shower curtain every couple of months than it would be to keep buying all that cleaning solution.

And then I thought, "Why didn't I think of that before?"

And then I thought, "Oh, shit... what else do I have a mental block about?"

I still don't know the answer to that last question. But it made me realize: we all have mental blocks about some things, and that, apparently, was one of mine: I was thinking of a shower curtain as a permanent fixture, and a bottle of shower cleaner as a consumable and, like I said, I only like to buy permanent fixtures once.

Since then, I've been trying to identify other brain failures on my part. I haven't found many, at least not of that amount of boneheadedness. But since I had one, I'm sure I have others; I just don't know what they are. And I don't have anyone in my life to tell me. My ex didn't explain her reasoning to me, perhaps not believing that I, a certified supergenius, could be so fucking stupid about something so basic.

That's the problem with cognitive biases: they're not obvious to the person who has them. Otherwise, they wouldn't be biases.

I got the last word in on the cleaner vs. curtain debate, of course; now that I'm single, I don't feel the need to spray down the shower. Though it does get a thorough cleaning once a month. Don't look at me like that; I hire a cleaning service for that sort of thing. It may not be cheaper than doing it myself, but it sure saves me a lot of hassle.

If you think you need to go
If you wanted to be free
There's one thing you need to know
And that's that you can't count on me
No you can't count on me

4 Like • Comment • View 8 comments

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