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 6 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 8 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.

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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.

May 5, 2021 at 12:02am

#1009675

Taking Off

PROMPT May 5th

If your job gave you a surprise seven day paid break to rest and recuperate, what would you do with those seven days?

I'm familiar with a company that does this sort of thing. Every so often they hold a raffle of sorts, and whoever wins the raffle is obligated to take some time off -- I don't remember if it's a week or three days or two weeks or whatever, but the trick is, that vacation time begins right now. Grab your stuff and head out the door. No calls, no texts, no work-related e-mails.

The point, as the employer explained to me, is twofold: One, it gives people a break, which is important as this is a finance company (that, by the way, is the only other clue I'm going to give as to the identity of the company), and you are probably aware of how stressful that industry can be.

The other reason is perhaps a little more double-edged: they want to hammer home the fact that no one person at the company is indispensable, that other people can step in and do the work if need be. So this raffle applies to everyone, from the CEO on down (though I'm guessing not to contract employees -- think, like, Uber drivers). The reasoning is that anyone could get hit by a bus at any time, and they don't want to get left holding the bag if one employee, even the CEO, doesn't have a backup plan in place. The dark side of this, of course -- the other edge -- is that this means that since no one is indispensable, they could lay you off at any time and barely feel it.

But meanwhile, hey, free vacation. Yes, if I recall correctly, it's paid time off. This is in addition to whatever their actual PTO policy is, which I'm not very clear on, but in finance it tends to be pretty minimal and discouraged. But I know they do get some.

With regular vacation time, one has the ability to make plans: buy airline tickets in advance, make hotel and rental car reservations, whatever. But you can't plan to win the Time Off Raffle (that's not what it's called, but again, I'm not naming names here), unless, I suppose, you figure out a way to cheat, which would make you an even bigger asshole than most financial services employees. So your options are probably a little more limited.

Now, I never worked for this company; they're just someone I do business with. But it did get me thinking about what I'd do with the time, so I can respond to this prompt as if I'm not retired and pretty much do whatever I want, whenever I want, anyway.

Given the nature of the company in question, I'd probably be tempted to stay home, sleep, binge-watch shows, and play video games. Maybe do some writing, but, mostly, sleep. There's a stupid goddamn portmanteau for this activity, which I hate so much that I'm not going to use here. It's cheap and there's no planning involved, and it is pretty much guaranteed to help one destress after a few months working in finance.

If I were feeling ambitious, I might use the time to look for better jobs, but I don't think they exist.

Another option, again if it were me, would be to do what I generally do on road trips: pick a destination at random -- I mean, really at random, not just say something like "I think Des Moines would be nice; I'mma go there" -- and take a road trip. No real planning is necessary, though it might help to check ahead to make sure there's not some festival or sportsball game at the destination that would sell out all the hotels. (I don't use AirBnB; they suck. Besides, you know all those scary "we used a black light in the hotel room and ew gross" videos? That's about rooms that are thoroughly cleaned; imagine how much worse an AirBnB run by some random schlub would be. I have a whole rant on this practice in my head; perhaps one day I'll get to use it.)

Of course, for me, such a trip would involve visiting all the breweries on the way to, at, and on the way back from, the destination; other people will have other priorities.

If your passport is up to date, perhaps you'd have other options, as well. I always thought it would be nice to take a spontaneous trip to, I dunno, Sydney or something. But foreign travel generally requires a bit more planning than domestic. And with what's going on in the world right now, I don't know if that sort of thing is even possible.

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