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 8 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 10 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 30, 2022 at 12:01am

#1034460

The 80s Called

Wrapping up June with this one from Cracked...

15 Weirdest Food Trends of the ‘80s

The title immediately caught my attention (clickbait!) because the 1980s was the decade I started out as a kid and ended up as a kid who was legally allowed to drink. It's hard for me to believe that the food trends of that decade could possibly be worse than the low-fat craze of the 90s, the no-carb fad of the noughties, or the utterly stupid gluten-free bullshit from the 10s. Or, for that matter, the abundance of aspics in the 50s, which, thankfully, I missed on account of not having been born yet.

The ‘80s were a crazy time for everyone, from the most powerful Gordon Gekko clones to those who were just trying to get their groove on but nevertheless had to wear stupid neon pants, and perhaps no one was more confused than food companies.

The only thing "crazy" about the 80s were the people running various world governments, especially our own.

Also, I never have figured out who the hell Gordon Gekko is, and I can't be arsed to look him up now.

Over the course of this decade that was mostly fueled by cocaine and hairspray, they apparently figured that what we actually ate didn’t much matter and took the opportunity to get weird with it.

Well, nothing mattered, because we were about to get nuked by Russia.

As usual, I'm not copying everything here, just hitting the ones that I have something to say about.

15. New Coke

Ah, yes, I remember this one well. I called it the Great Coke Crisis of 1985, and it was truly a dark time. I tried that piss once and spit it right out. It was almost as bad as Pepsi, if you can believe it. I got hooked on Dr. Pepper that summer.

But it's not weird. Unfortunate, sure, but not weird.

14. “Light” Drinks

The success of Diet Coke in 1982 perhaps led the company to fly too close to the sun. It kicked off a whole slew of “light” drinks, like Crystal Light and Bud Light, in response to the burgeoning health craze.

And this is different from today how?

11. Tie-In Foods

The height of commercialism brought with it the height of pop culture or celebrity tie-in products.

These were around before the 80s and stuck around long after.

8. Hubba Bubba Soda

Okay. Okay. I'll grant you this one. I don't think I could have nightmared up a more ridiculous abomination against all that is holy than a soda that tasted like bubble gum. I will say this, though: I lived the 80s, and this is the first I ever heard of HBS.

That, or I gave myself deliberate amnesia about it.

As an aside, I was introduced to the concept of urban legends in the 70s, when there was one going around that Hubba Bubba (whose claim to fame as a bubble gum was that it was soft and chewy, not a brick like the old standby, Dubble Bubble) was made with spider eggs. I mean, come on, even Kid Me couldn't have believed that shit.

6. Tobacco Gum

Okay, look, no, this wasn't tobacco-flavored chewing gum, but shredded gum that was supposed to resemble chewing tobacco (to a moderate extent). I saw it as an alternative to chew, but the Morals Police eventually freaked the fuck out just like they did with candy cigarettes a decade earlier, which I also thought was bullshit. I mean, those things were nasty, regardless of whether they were "training" kids to smoke.

2. The McDLT

You know what? Screw you. Those bastards were delicious.

It was obscenely wasteful, totally unnecessary, and mostly ineffective. It was perfectly ‘80s.

That much, I'll grant.

So anyway, like I said, there's more at the link, but they didn't impact my life in any significant way. Okay, neither did #8 (I swear I had no idea that hippo diarrhea ever existed until I read this article), but that one's notable in that I'd at least heard of all the others.

I'll just end this with the usual reminder: in 40 years, people will be looking back at our food trends today and making them into weird food lists.

They should start with "hard seltzer." Or, they could, if that crap wasn't just rebranded Zima from the 90s.

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