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!

about 8 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 10 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.

July 18, 2020 at 12:06am

#988445

Gnaw Bone

How come it's never a girlcott?

PROMPT July 18th

Have you ever boycotted a company or product? If so, tell us the story. If not, what would a company have to do for you to boycott its products?

My big decision for the day was this: beer, wine, scotch, tequila, gin, rum, or other?

I went with wine.

A few years ago, on one of my cross-country expeditions, I passed through a tiny spot in Indiana called Gnaw Bone.

This made me laugh.

On another cross-country expedition, I found myself driving through Gnaw Bone again, and this time I decided to stop. There is a winery there. One of their products is called Chateau Gnaw Boné, which is a cranberry-apple-brandy Frankenwine. I picked up a bottle and took it home.

Tonight was the night to drink it.

The funny thing is, there's some debate over how Gnaw Bone got its name. My personal theory? As with many other place names in Indiana, such as Terre Haute, Lafayette, Versailles, etc., I think the town - village - wide spot in the road - whatever was originally a French place, in this case named Narbonne.

Because Americans can't pronounce French for shit.

Anyway. This shit is 23% ABV, and even with the help of my housemate, I'm definitely feeling the effects. So here's my attempt at actually addressing the prompt.

I have not participated in an official boycott.

Oh, I'd like to say I'm boycotting Chick-Fil-A or whatever because of their policies, but this means jack shit because I'd never eat there anyway.

Starbucks, to take another example, could disappear from the face of the planet and it would make zero difference to me, because I've been to one, like... twice?

Thing is, I'm not going to inconvenience myself over petty political differences. I just don't give enough of a shit. Your factory employs people making $1 a day or whatever? Well, then, let's all decide to stop buying from that place and make sure the people make $0 a day instead. That makes sense.

That was sarcasm.

Ask me again when I'm sober and I'll probably have a different answer. But right now, I couldn't care less if you paid me to.

So to answer the last part of the prompt, you pretty much have to be an unutterably fascist piece of shit for me to boycott your products. But chances are I pick up on that before it becomes public, so my refusal to buy shit from you makes zero difference. Like, I've never liked Donald Trump, regardless of politics, so I refused to go to his winery, which is near here. Now, as you know, me refusing alcohol is like, well, someone in the desert refusing a drink of water. But I couldn't boycott his wines after he became president because I never drank them in the first place.

For all I know, the owner of the winery in Gnaw Bone, Indiana has political views I disagree with. I don't care. I'm still using his or her products to get drunk on.

On that note, I'mma finish this bottle of wine. Because this prompt made me talk about politics, which I hate to do.

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