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').

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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.

September 20, 2019 at 12:08am

#966475

Dealing With Trolls

PROMPT September 20th

The prompt today is from WakeUpAndLive~doingNaNo'24

!

Have you ever experienced hateful comments on the Internet? How do you deal with shaming, blaming, and intolerance?

Sure, hasn't everybody?

Long ago, I developed a personal policy of utterly ignoring trolls.

This serves two important purposes: One, I don't get my balls all in a knot, because I pretend the hater doesn't exist. And two, the one thing that trolls want more than anything else is attention, and this deprives them of that. I like to imagine their heads exploding all over their mothers' basements.

You'd think such a thing would be easy. It's not, always, though as with other things, it gets easier with practice. When someone is wrong on the internet

, the natural human response is to engage with that person, show them why they're wrong, and make choice comments about their parentage (or lack thereof), personal hygiene habits, sexual practices, and afterlife destination.

There's no point.

You're not going to change someone's mind, and most of the people doing the hateful stuff don't want their minds changed. Hell, some of 'em don't even believe what they're saying. They're just doing it for the lulz. And the attention, but mostly for the lulz. If they can get a rise out of you - or any response, really - they've won. You've lost.

The only way to win is not to play.

If everyone adopted this policy, the trolls would wither away and die. Well, metaphorically. They might at least go somewhere else, mill amongst their own kind for a while.

It's even more difficult when it's not directed at me personally. Racist or sexist comments, for example; that sort of thing. But I've rarely seen that behavior and been in a position to do anything about it. I mean, sure, if it happens here on WDC there are actions I can take, but we don't get that a lot here, at least not for very long.

And I don't like blocking people. I want to hear what they have to say, even if it's hateful. Otherwise, they're speaking behind my back, and I don't much like that, either.

We've developed social practices around the idea that we're meeting face-to-face. Things are different online. The people on the other end of the internet are real people, sure, but we're under no obligation to engage with them if we don't want to. This is not to say that we should all just hang out with like-minded people exclusively, but there's no reason to tolerate intolerance.

4 Like • Comment • View 2 comments

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