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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 10 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 12 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.

March 17, 2022 at 12:01am

#1029050

We Have Met the Enemy

I wanted to talk about generational warfare again, but fortunately, I don't have to, because this author is doing it for me.

Ageism. The Final Frontier For People Too Woke to Be Racist Bigots
Okay boomer is not okay

Now, again, I don't hold a lot of stock in the whole generations thing. While there's some use to defining cohorts, in practice, you get what this article describes: yet another way to keep us fighting each other instead of the real enemy (spoiler: it's the system, man).

Masking insult with humor wasn’t funny then, and it’s not funny now.
You aren’t funny, and you aren’t joking.

There’s a problem with masking insult as humor. Two problems.

First, it dodges responsibility. The person making the “joke” doesn’t even have to cop to their prejudice.

Secondly, when you mask insult as humor, it reassigns blame on the person being insulted. Say the magical “it’s a joke” words and you don’t even have to cop to being rude. Or ignorant, or uninformed, for that matter.

There's a term for this: Schrodinger's Asshole

. Which has nothing to do with the nether regions of a famous physicist, and everything to do with deciding whether or not you were kidding after you make an insensitive "joke."

Show me someone who says “ok, boomer” and I’ll show you a dyed in the wool woke person, complete with rainbow flag on their Facebook every June.

Somehow, they get #BlackLivesMatter and #metoo. They believe in gender equality, climate change and every other social issue.

Except ageism.

Because, boomers screwed them. Right?

I've had in mind for a while now that there's something about human nature that absolutely requires that we have a group to look down on. No matter how shitty your life is, no matter how the world has screwed you, you can at least take comfort in not being one of those people.

We're running out of groups to shit on, though. Even with those perennial scapegoats, the Jews, you're still going to get called out for ragging on them.

But some groups are still fair game. The fat, for instance. And the old.

Young people today have been screwed out of a future. That part, they got right. If you’re a young person today, here’s what you’re facing.

— You can’t afford to buy a house.
— You’re going to have at least 13 jobs in your life, if not more.
— There’s not going to be a gold watch or retirement party
— There’s not going to be any pension left for you.

Oh, it's worse than all that.

Unless the world ends first, because the entire planet is burning and flooding and the insects and animals are dying and and too many people think their uneducated hot take is equal to the opinion of someone who is educated. Because freedom of speech!

This author is way more optimistic than I am.

You think you’re woke, but the truth is you have no clue. No idea how we got here, much less who to blame. You see how f — cked up the world is, and blaming boomers is easy.

You didn’t invent that, either.

Ever heard of hippies? Back in the 60’s, hippies wore love beads and peace signs and screamed about global warming and fat cats and insisted you can’t trust anyone over 30.

Yes, the generation you're ragging on now is the one that protested Vietnam, fought for civil rights, and tried to push the Equal Rights Amendment through the states.

Pretending the problem can be blamed on a generation is delusional at best and destructive at worst. You can’t fix what you can’t see.

The problem needs fixing. Very, very badly.

Ain't nothin' gonna happen.

The problem is corporate wealth hoarding at the expense of the worker.

And right now you've lost half your readers who have just snorted, "SOSHULIZM"

Anyway, the rest of the article goes on like that, pointing the finger where it belongs. Not just "the rich," but the whole exploitative system.

Because it was never an age. To the rich, your poverty isn’t a bug, it’s a feature. If you can understand that, maybe you can begin to affect change.

Effect. Maybe you can begin to effect change. But bad grammar isn't really the problem; it just annoys me.

Not only do we have to have some group to use as a scapegoat, but I'm leaning more and more to the idea that the system -- not just capitalism, but every economic system ever developed -- has to have people to exploit. People desperate enough to do anything to get by. If everyone had a real choice in where they worked, how many would become sanitation workers? How many would choose to do the grunt work, the low-paid, mostly ignored, necessary things to keep society functioning? No, you take a shitty job only when there's no other choice. That's why they call it a shitty job.

Anyway, maybe people are finally waking up to that. What it's going to be replaced with, I don't know. But we have to have our cogs in the machine, so I'm pretty sure it's not going to be very nice.

Won't affect me much. I missed the cutoff for Boomers by a year or so; my defined cohort hasn't been blamed for anything yet. But I'm old enough that I'm just not going to fight anymore; it's not my war. So, once again, I end with the rallying cry of my generation:

Meh. Whatever.

4 Like • Comment • View 3 comments

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