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!

a day 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

a day 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.

May 14, 2019 at 12:57am

#958910

Burned Out

Discuss the “Four Burners Theory” as it is outlined in this website:

https://jamesclear.com/four-burners-theory

Which burner in your life burns the brightest? If you had to completely turn off one of your burners to be successful in the other three, which would you turn off?

Calling that self-help-seminar ejaculate a "theory" is an insult to the entire institution of science.

A theory is not just a guess or a way of looking at things - we have other words for those. No, a theory is a system that is supported by evidence and can be used to make further inquiries. And when those inquiries contradict something in the theory, the theory changes. This? This is little more than a philosophical metaphor, and as philosophical metaphors go, it's woefully inadequate.

But let's work with it, for now.

At the moment, I have exactly one burner going, and it's on simmer: the health one. So maybe I'm not the one to address the article's points. But, as this is my blog and it has me fired up (pun, as always, intended), I'm going to do it anyway.

The first burner represents your family.

"Family" can mean many things, but this particular article plays the "you're going to have kids" card, and it's clear that "family" means "offspring" in this context. Well, I sidestepped that one neatly, didn't I? My answer to work-family balance? Don't reproduce. Kids just aren't worth the time, energy, effort, or money. I read somewhere that it takes half a million dollars to raise a child through the end of high school, if you're a middle-class American (to be fair, there aren't many of those anymore). Used to be they were useful, when most people had farms and whatnot and they could provide free labor. These days, you can't even have one mow your lawn without horrified looks from other people.

The second burner is your friends.

I've mentioned before that I'm an introvert. This doesn't mean that I have no friends; it means that I have fewer "friend" relationships that I nurturemaintain to the best of my limited ability. We do stuff together. I stay away from high-maintenance people. This pretty much takes care of itself.

The third burner is your health.

This is the one I say I have on simmer. I didn't have it on at all for a long time, so I had a heart attack. Even after that, I didn't turn it on until fairly recently. I'm still surprised at how successful I've been at following a regimen that has caused me to lose some weight, though I have a long way to go. But I work on this oh, maybe two hours a day: a bit over an hour to go to the gym, and a bit under an hour to prepare meals.

The fourth burner is your work.

Work, to me, was always about one thing: amassing enough money so I didn't have to work. So I don't work anymore. When I did, everything else kind of fell by the wayside, because that often happens when one owns a business. Even before that, while I wasn't what you'd call a workaholic, I did work far more than the formerly standard 40 hours a week. This cost me two marriages. And now that I don't have to work, I'm deliberately single again. Life is strange.

“in order to be successful you have to cut off one of your burners. And in order to be really successful you have to cut off two.”

What the sodding hell does "successful" mean? Okay, I guess I was successful, because I'm mostly where I want to be right now. You define your own success. Money? Family? Living to 110? Partying? Those each relate to one of the "four burners." My success isn't yours. As noted in the article, "Most entrepreneurs, artists, and creators I know would feel bored and without a sense of purpose if they had nothing to work on each day." Well, I never feel bored, and I frankly don't need a sense of purpose, so like I said, work to me was always nothing but a means to an end. Other people, I understand, are different.

nobody likes being told they can't have it all, but everyone has constraints on their time and energy. Every choice has a cost.

Well, fucking DUH. But the converse is also true: every cost has a choice. No one can have it all. I've said it before, and I'll say it again: it's not about having what you want.

It's about wanting what you have.

6 Like • Comment • View 9 comments

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