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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Write_Mikey_Write!

about 3 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 5 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.

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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 7, 2020 at 1:30am

#992611

You CAN Take It With You

What is this "productive and happy" of which you speak?"

PROMPT September 7th

I completely rearranged my desk space yesterday! It was a much-needed change and has helped with my motivation. What does your desk space / writing space look like? What sorts of things do you need (or not need) in your work space to be productive and happy?

Here's the thing: I like being in a clean, organized space.

Here's the other thing: I despise cleaning and organizing with every fiber of my being.

These two urges tug constantly at my psyche, just like "eating that whole pizza" vs. "not having another heart attack." Sometimes one wins. Sometimes the other does. Most of the time I just distract myself with something else.

Anyway, I don't have dedicated desk space right now. My office has gathered too much crap, and I can't be arsed to straighten it all out. I write on a laptop, because a) I travel, or I used to in the Before Time, and b) I like to sit outside on my deck whenever it's not too cold. Too hot, I can deal with. Drop below about 70F / 21C, though, and I start to freeze to death.

I'm not looking forward to fall and winter.

Anyway. it's a honkin' big laptop, because I also use it for gaming. Not light, and I've seen cinderblocks smaller than the size of the power converter. Still, it's portable enough to fit into my backpack for travel, if that ever becomes an option again, and no one wants to steal the backpack because it's heavier than a box of rocks.

One of the things I like most about traveling is hotel rooms.

I know this is probably just as unrelatable to most people as my desire for heat over cold. Hotel rooms freak a lot of people out. Me? Love 'em. Even the dingy, faded ones. I've been in those, and I've also stayed at the actual Ritz-Carlton. And everything in between. Because I walk into one, and it's sparse: A bed or two. Bathroom. A nightstand with a lamp. A dresser. A desk and chair. A TV which I utterly ignore. One of the reasons I don't usually travel with people is every time I do, they seem to have this need to walk into a hotel room and immediately turn the TV on. It's annoying as hell and I don't understand it. All TV can do is provide us with commercials and other chaotic noises.

But I digress. A hotel room looks clean and neat. It may not actually be clean, but I don't give a damn. Best of all, I'm not the one who cleaned it. I pay for that privilege gladly. So then I can set up my excessively-sized laptop on the desk, plug it in, and game, or write, or look at cat videos, or whatever.

Now, look, I don't want to give anyone the idea that I'm a lazy bum who expects other people to do his housework for him. No, I'm a lazy bum who hates to do housework, and hates even more if someone does it for me -- except in the aforementioned hotel rooms. I neaten up when I have to at home, but not before. Usually I just take the laptop outside, as I said, where I can't leave a lot of shit lying around because sometimes it rains, snows, or winds.

Productive and happy, though? Pipe dreams.

Final Birthday Week MB goes to WakeUpAndLive~doingNaNo'24

as a fellow Trekker, but please know that I appreciated all of the comments. Yes, all of them. Thank you. Some things coming up this week: Tomorrow is Star Trek Day, which commemorates the anniversary of the first airing of the first Original Series episode on September 8, 1966; September 10 would have been my father's 103rd birthday; and then September 11 is, among other things, my account anniversary. Hopefully I'll remember to give out more Merit Badges for my account anniversary, if I don't drink too much rum the day before (Dad was a sailor).

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