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!

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.

September 17, 2019 at 12:11am

#966303

Comfortable

PROMPT September 17th

Today’s prompt is from NaNoKit

!

Did you have a comfort blanket/toy when you were little? What comforts you now?

The tears of my enemies.

Didn't everybody have a comfort thingie when they were a kid? I distinctly remember having a teddy bear. I don't know that I ever named it. No idea what happened to it. Probably "went off to live in the country." Oh, wait, my parents couldn't use that particular lie; we lived in the country already.

Recently, I was reading one of the science blogs I follow, and the guy posted a picture of the teddy bear he had when he was a kid. And this guy's quite a bit older than I am. I tend to keep things way beyond their usefulness, but not that. Very likely, my parents decided for me, like they did with my first comic book collection, for which I can never forgive them.

When I was 4, my parents obtained a collie. I suppose she would count, as well; she always slept near my bed. I named her "Lassie" because I was fucking four, okay? Oh, who am I kidding; I'm no more creative with names now than I was back then.

Only dog I ever had, that one. Lassie was a good dog. Had to be, to put up with kid-me.

I don't know if this counts as a comfort thing, but I can't sleep right unless there's a blanket. Even when it's really hot - which it hardly ever is, because I'm civilized and have climate-change-inducing central air conditioning - I have to have at least a light blanket. A sheet won't do. And yet, I kept sleeping with blanket-hogging chicks. My solution was to have an emergency blanket of my own. Bad enough to get into fights when you're awake; you don't want to do it when you're half asleep. Anyway, it doesn't matter much which blanket; any will do, even the shitty ones in hotel rooms.

I hear people talk about "comfort food" all the time. Honestly, I don't quite get it. Either I like a food or I don't. Since I've been restricting calorie intake, I haven't been eating my usual foods, and while I miss things like grilled cheese sandwiches, it's more about taste than comfort.

Pretty sure Brussels sprouts isn't anyone's comfort food.

Oh well, off to cook some Brussels sprouts.

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