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.

June 10, 2021 at 12:03am

#1011579

Lazy-er Light

Today's article is basically a book promotion, but whatever -- it still has what I consider to be good information.

5 Tips for Resisting the "Laziness Lie"
No one chooses to fail or disappoint. We need to unlearn our bias of laziness.

Being a lazy person, I thought this might be about how to be not-lazy. Boy, was I wrong. It's tips for how to be more lazy, as if I didn't already have great role models for that: my cats.

The book explores how our culture’s fear of laziness is rooted in unjust historical systems such as enslavement and the belief in the Protestant Work Ethic, and how such beliefs lead to overwork, exploitation, and alienation.

Huh. So that's an elevator pitch, and a damn good one: one sentence, succinct, a summary of the main points. And it especially appeals to me because I've been part of the RAPWE (Resistance Against the Protestant Work Ethic, an acronym I just now made up) for years.

For anyone who doesn’t have the energy—or time—to read a full book about how busy and overworked we all are right now, here are five key insights from my book you can read in a single sitting:

And that's how you do a book self-promotion: don't just tease us, but give us some solid points from the text. Sure, some people (like me) will still be too lazy to buy the book, but you're still shilling it to a larger audience than you'd otherwise have.

1. "Laziness" isn't what you think.

The “laziness lie” is my term for the set of unspoken, deeply held cultural beliefs that each of us absorbs throughout our lifetimes about the value of work and the danger of “laziness.”

There seems to be a rule in self-help books -- maybe even psych books in general -- that the author has to come up with a catchphrase to center the text around. Preferably one that rhymes, alliterates, has a pun, or some combination thereof

The laziness lie tells us that our worth as human beings is linked to our productivity, that our needs and limitations cannot be trusted and must instead be ignored, and that, no matter how busy we are, there is more that we should be doing.

Yeah, again, I've resisted that shit since practically Day One.

2. When you feel “lazy,” you’re doing too much.

For my book, I interviewed some of the busiest, most stressed, most burned-out people... What I found across the board was that each extremely busy person felt like a failure and was somehow convinced they were lazy.

Newsflash: Most of us are crap at self-diagnosis.

The answer is to stop buying into the laziness lie and start reframing how we set priorities in our lives. When you feel like you’re not doing enough, the answer is to find something to cut back on or let drop.

Hm... I don't know... what should I cut back on? Playing video games or watching TV shows?

3. You aren’t “wasting” time. All your time is accounted for.

Decades of productivity research shows that, at most, the average worker can only focus on job tasks for about three to four hours per day.

I guess I brought that average down single-handedly. My limit for focusing on job tasks was approximately three nanoseconds.

4. Embracing consent means rejecting "lazy."

In a culture that hates laziness, it is difficult for a person to assert their boundaries and confidently say “no” to anything.

Huh. That's odd. I get told "no" all the time.

If we want to resist the laziness lie, we need to learn to embrace our feelings, including emotions like apathy and annoyance, which people often don’t like facing in themselves.

It is true that once I initially ran out of fucks to give, my life became ten times easier. Apathy is power.

5. Action isn’t morally superior to inaction.

In a world shaped by the laziness lie, work is equated with goodness, and doing “something” is almost always seen as superior to doing nothing. This leads to a lot of problems, like activist fatigue or activist frenzy, where people are constantly posting misinformation and poorly researched calls to action online because they are so desperate to want to do good.

Hm... I've been assuming that most of those calls to action are cackling Russian trolls doing social engineering.

We don’t have to be heroes, and we don’t constantly need to go go go. We can take a step back and cultivate relationships instead.

The only relationship I want to cultivate is with my bed. Sometimes I cheat on it with the couch.

Anyway, clearly none of this advice is useful to me (hence why I'm not rushing over to Amazon to buy the book), but I hope today's double whammy of "how to write a book pitch" and "how to get on your ass and be lazy" will be of benefit to someone reading this. That is, of course, if you made it this far and didn't give up out of laziness.

6 Like • Comment • View 4 comments

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