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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Write_Mikey_Write!

about 3 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 5 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').

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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

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

September 24, 2020 at 12:03am

#994053

Ex-Spend-Able

Today's prompt reminds me of an old joke.

PROMPT September 24th

If I gave you $5000 and told you that you had to spend it today, what would you buy? (Have fun with this one

)

Telling the joke from memory since I can't be arsed to look it up.

A rich dude was dating three women. One day, he decided it was time to settle down and pick one, so he gave each of them $5000 to see what they'd do with it.

A week later, the first one comes back with a bunch of boxes. "I spent the $5000 on things I know you'd love. Power tools, lawn furniture, a barbecue grill and supplies, a giant TV, that sort of thing. I wanted to show you how much I care about your desires."

The second woman shows up all different-looking. "I spent the $5000 on a complete makeover, hairstyle, new dresses, and such, because I wanted to show that I want to keep myself looking good for you."

The third one comes back and slaps $10,000 on the table in front of him. "I invested the $5000 in the stock market and doubled the money in a week, because I wanted to show you how good I am with money."

Well, the guy thought about it, considering the various merits of each of their activities, and he thought about it some more, and then thought about it even more, and he married the one with the biggest tits.

Now, I don't want power tools or any of that crap (at least beyond what's needed for a particular project), and I don't care all that much about looks. So those are right out for the purposes of today's prompt.

I don't suppose I could simply invest the $5000? No? Argh. Well, the prompt did say "spend," so I'm guessing no, but if someone actually gave me $5000 (I take PayPal), I'd put it in the stock market. I could do all that in one day, easy. None of this "doubling it in a week" nonsense, either; that's not investing but speculating, and speculation is gambling.

Not that I haven't done it. Just not with a whole lot of money.

Speaking of gambling, another option would be to hop on a plane, take it to Vegas and play high-stakes blackjack. Yes, blackjack -- I don't like poker, and roulette is too random. With blackjack, I have a system. Sometimes, the system even works.

But no, gambling isn't the same as spending. While I'm in Vegas, though, I could always find some hookers and blow, and... nah, I'm not really into hookers and/or blow, so that's not going to happen. But if it did, I could definitely do that in one day.

One thing I'd consider is one of those all-inclusive vacations, one that requires the money up-front. Spend it today, take the vacation whenever (preferably after there's a vaccine). But I think I have a better idea.

This stuff

is listed at about $5400 right now. I could pony up the extra $400. Or, if that's not allowed by the rules, well, I'm pretty sure there are other premium whiskeys for less than $5k. Hell, if I wanted to poke around a bit more on the internet I could find the Yamazaki for less; that was just the first result I found. Okay, no, it was the second, but the first was $10K so I'd have to wait until the money doubled in the stock market, which violates the conditions, so... nevermind.

Assuming I could find it for, say, $4000 (which I've seen it at before in the past), I'd spend the other $1000 on beer. Or maybe an assortment of beer, wine, gin, and tequila. No other whiskey, though; after drinking the Yamazaki, I think sullying my lips with any other whiskey would be dishonorable. Yes, even Pappy van Winkle. Thanks to websites, I could do all that in a day...

...oh, but wait. Virginia has stupid, idiotic laws about buying liquor online. Beer and wine, sure, with some limitations, but here, the state sells the hard stuff and they don't like competition.

And I'd be hard-pressed to find a beer that costs $5000. Getting a large quantity of cheaper beer is out, too, because not even I can go through it fast enough to drink it all before it gets skunked. I'd rather waste money than beer.

Wine, on the other hand... I've seen bottles of wine go for five figures, and I'd bet there are some that sell for more than that. It wouldn't be too hard to find a rare vintage that costs in the neighborhood of $4-5 K. And I could still make up any difference with an assortment of other tasty beverages.

I mean, sure, I *could* cart the cash down to the local animal shelter, or a charity for the homeless, but I don't think that would be considered spending it, either.

So, wine it is.

What? Was anyone really expecting me to settle on something that doesn't involve alcohol?

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