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 9 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 11 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.

February 16, 2022 at 9:17am

#1026805

Putting the Product in Productivity

I'm still in NYC, so another short one (this post, not the article) today -- one I don't quite know what to say about, but I'm going to try anyway.

the diminishing returns of productivity culture

Article is from last year, but I doubt there's much contextual difference now.

Like most of these kinds of articles, it opens with an anecdote of sorts. Which isn't bad in itself; I think it's a great way to hook a reader. It just doesn't have a lot that I can quote here, so I'm skipping it even though it's kind of important.

I thought about this passage this week, while working on the chapter in the new book on the history office tech that promised to make workers’ lives easier, but usually just created the compulsion to do more work. Much like the digital technologies of today, these technologies — from “24 hour computer lieutenants” in a GE dishwashing factory to word processors — were sold to workers as a means of making their work simpler, more predictable, safer.

You know what I remember from the 70s, maybe on into the early 80s? Someone promised we would have a three-day work week, or something to that effect, because computers and automation would help us get our jobs -- for various definitions of "our" -- done faster, leaving us more time for fishing. Imagine my shock and dismay when not only did that not happen, but employers started demanding more time out of us than during B.C. (Before Computers). In other words, not only were we compressing what used to take a week into a day; not only were we then expected to do five weeks' worth of B.C. work in a week, but we had to push it to add overtime and weekends.

Of course, we were also promised flying cars, so I suppose I should have known better.

Anyway, the article doesn't address that directly, I think, but it has a lot more to say than I'm going to relate here because, as I implied, I have a lot of other stuff to do today.

This is the dystopian reality of productivity culture. Its mandate is never “You figured out how to do my tasks more efficiently, so you get to spend less time working.” It is always: “You figured out how to do your tasks more efficiency, so you must now do more tasks.” Sometimes, if you’re a Wall Street investment banker, you can complete infinitely more tasks until you have so much money that you don’t even need it anymore — you’re productive for the thrill of it, but also because you don’t know how else to gauge your own self-worth.

My motivation was never productivity, though I did derive some satisfaction from completing a project. No, I only worked for one reason: to accumulate enough money such that I wouldn't have to participate in the productivity hamster wheel.

Obviously, different people are motivated by other things, and I'm not ragging on them here. Just on the culture that tries to squeeze more and more out of its workers until, like an empty tube of toothpaste, they just have nothing left.

The vast majority of people are not paid enough for the productivity that is demanded of them. More money can be stabilizing — and quiet the financial stress that interferes with productivity. But it doesn’t solve the fundamental problem: human productivity has a ceiling. Technology attempts to modify that reality, but it can only do so much. The body, and the mind, begins to falter.

And now, I'm off to be unproductive some more.

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