Complex Numbers (Book)

Blog Calendar

◄ July ► 2021
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

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.

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.

July 29, 2021 at 12:01am

#1014694

Chill

I don't usually draw from this source, and hopefully you'll see why.

What Is Toxic Productivity? Here's How To Spot The Damaging Behavior.
The pandemic has convinced us we have to be useful at all times. Here's what that mentality looks like, and how to deal with it.

Think about your work ethic during the pandemic. Have you been more productive than usual? Do you rush to volunteer for projects at work, even when your plate is already full? Do you promise to make dinner as soon as you finish “one last thing” on your to-do list? If you answered “yes” to any of these questions, you might be suffering from toxic productivity.

No, no, and no. There, done.

My work ethic used to be stronger, but nothing good ever came of it, so I abandoned it. For some people, though, this ill-defined concept of "hard work" keeps them sane. Newsflash: everyone is different.

In many ways, “toxic productivity” is just a buzzy new term for workaholism ― but it’s also a little more nuanced than that old-school phrase. Toxic productivity is essentially an unhealthy desire to be productive at all times, at all costs.

I hated that old term too, as well as anything that gets tagged "-holism." Similarly, stop tagging "-gate" on every damn scandal.

Toxic productivity doesn’t even let up once the task is complete. Once you’re technically done with a project at work, you might feel guilty for not having done more. For the afflicted, too much is never enough, said Simone Milasas, a business coach and author of “Joy of Business.”

Is a "business coach" something like a "life coach?" Or is it some weird hybrid airplane ticket?

Many of us have fallen into patterns of toxic productivity during the pandemic, said Kathryn Esquer, a psychologist and founder of the Teletherapist Network. That’s primarily because all of our regular routines were put on pause. All of a sudden, we had unprecedented amounts of free time.

"Many?" Any chance of being more specific here? Also, where did that "free time" come from, removal of commute?

But why did we throw ourselves into work instead of seizing the opportunity to be blissfully, guiltlessly idle for once?

And what's this "we" shit? My routine barely changed -- though I admit I'm an outlier.

We didn’t stop once the workday ended, either. We told ourselves we’d learn a new language, become an expert baker or master some other skill we’d put off learning in the Before Times.

I have been learning a new language. I started two years ago, before the pandemic. And dammit, I'd demand royalties on the phrase "Before Time," except I stole it from a Star Trek (original series) episode.

As one viral productivity-pushing tweet put it: “If you don’t come out of this quarantine with either: 1.) a new skill 2.) starting what you’ve been putting off like a new business 3.) more knowledge [then] you didn’t ever lack the time, you lacked the discipline.”

And once again we see the cesspool that is Twatter. First of all, "either" implies two choices, not more; second, we should be shooting for "more knowledge" all the time.

Work culture in the United States valorizes the grind ― and in moments of crisis, we grind all the harder. Look at World War II and the vast, rapid expansion of U.S. civilian manufacturing capacity to meet wartime demands.

That was top-down, not bottom-up.

The first step is to recognize that you have a problem.

Oh? Are there eleven more steps?

“One sign of toxic productivity is calling for a Zoom meeting when certainly a phone call or email would be OK,” she said. “Another is using of lot of jargon that makes the conversation twice as long because you’re afraid of how it will look if you’re brief, concise and just move along.”

Oh, and here I thought those were both signs of "being a manager."

Once you wrap up one project, do you give yourself a well-deserved break, or do you run to the next project with little thought? Are you constantly asking yourself “What should I be doing now?” even when it’s the weekend?

That question is a sign of textbook toxic productivity, Milasas said. She said a better question to ask yourself is: “What could I do or create with ease now? What would it take to create this with zero stress?”

I can always play video games or watch old episodes of Star Trek.

What’s funny about toxic productivity is that it exists more in our heads than in our actual work environments. In other words, there are very few bosses out there who care if you’ve been working hard around the clock, Ruettimann said.

Is that so? Then how come those same bosses monitor your keyboard and camera time?

And again... what exactly the fuck is "hard work?" Farm hands work hard and twenty years later, they're still hard-working farm hands.

Americans have a notoriously bad grasp on work-life balance: We’re loath to take our vacation days. We’re overworked, especially during the pandemic. We send unnecessary emails over the weekend. We simply can’t log off.

Again, what's this "we" shit?

Okay, to be fair, I'm sure there are a some people who need this advice. For others, it can be safely ignored. My biggest issue is how it's presented.

But unless you have a specific goal in mind, working extra hours is just counterproductive. That goal could be "keeping my job," but do you really need to keep a job that makes you work 80-hour weeks?

It's time the workers fought back, and not just in the service industry. Rise up! You have nothing to lose but your chains.

Once again, I failed to do this review yesterday for a movie I saw on Tuesday.

One-sentence Movie Review: Old

While I can certainly understand anyone's trepidation for seeing another Shyamalan movie, this one is done well, with brilliant acting, seamless effects, and remarkable camera work, although it does stumble a bit in some places; the trademark MNS "twist" isn't the movie's whole gimmick, and while it's not what anyone would call realistic, that's never been a requirement for a horror movie.

Rating: 4/5

Next week, I'll take on The Suicide Squad.

8 Like • Comment • View 5 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.