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 5 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 7 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.

December 1, 2023 at 12:43pm

#1060387

Travel Advice, Part 3

When traveling, it's important to be aware of local customs. For example,

Pronunciation

When traveling around the US, you need to be aware that, often, place names aren't pronounced the way you'd think based on the usual rules of English. For example, there's a town near where I live called Staunton. You'd think, looking at it, it's pronounced stawn-ton, right? No, it's pronounced che-vee. Okay, no, just kidding; it's stan-ton, with an a like in hat.

Worse, though, are places that are pronounced like you'd expect in English... but they're Spanish or French. Like, if you pronounce Versailles, Indiana, as if you'd just stepped off the plane from Par-ee, the locals will kick your derrière all the way to Illinois (a state whose name is pronounced like the French would).

But you just never know, so unless and until you're absolutely, 100% certain of something's pronunciation, usually by hearing a local speak the word, it's best to not mention the name at all. Some folks don't take kindly to strangers, and their best way of identifying a stranger is by their mispronunciation of the local town, street, or dive bar.

Like, in my hometown, we have a Rio Road. I can always identify the tourists because they pronounce it like Rio de Janeiro or Rio Grande. But no. It's pronounced like rye-oh. Don't ask me why; I just know we use it as a shibboleth so we know who to send to the more expensive restaurants.

As I said, though, you never know. You could have a place in the US named some common, easy-to-pronounce English words like, I don't know, New Haven, and it'll turn out that Haven is pronounced like havin'. As in, don't bother me, I'm havin' lunch. As far as I know, that's not the case with the one in Connecticut, but you know it could happen.

Or, like, I can see myself visiting a small town with a common name, and someone asks "How do you like it here so far?"

I'll be like "Oh, it's nice. I really like Riverside."

And their face will immediately close up and they'll look sideways at me with great suspicion. "It's 'reverse-a-dee.'"

Look, I'm just saying I wouldn't be surprised, okay?

5 Like • Comment • View 4 comments

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