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 9 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 11 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.

June 28, 2021 at 6:35am

#1012648

Bloomington

Another ambiguous reference. I could put the state in the title, but what would be the fun in that? Anyway, I mean the one in Illinois, not the one in Indiana.

Hey, at least it's not Springfield. Then it could be any state. Sometimes I think it would be fun to visit every Springfield in the country, mostly to see how many of them were actually named after spring fields and, if so, how many of those have been paved over (my guess: all). But I'd get really tired really fast of all the Simpsons jokes.

Lots of places are like that, you know. You name a place, I dunno, "Oakville," because there's a shit-ton of oaks there, and then you cut down all the oak trees. Then people come to the town, look around, and are like "Why is this called Oakville." "Well, because of the stand of oak trees" "What stand of oak trees?" "Oh, we cut those down years ago." Or you call a city "Peaksville." "Is it named after some guy named Peak?" "No, it's after the mountain." "What mountain?" "The one we leveled to build the city."

Point is, it's extraordinarily rare that whatever they've named the place after is still there today. This is trivial in the case of, say, New York, named after a long-dead Duke of York, but, like... hell, I don't know... the town of Woodbridge, Virginia doesn't have a wooden bridge anymore. Or maybe it does, but not the one it was named after.

Bloomington is kind of like that. According to this,

anyway, it was named after a grove (of unspecified type) called Blooming Grove (so, presumably, some variety of angiosperm). Whether the grove is still there or not is unclear, but I'd put money on "not."

Not that it's a big city or anything. It's actually quite nice, from what I've seen, and you might have noticed that I met Sum1's Home

for dinner and beer at a truly excellent local brewpub. Here's the note he posted, including a very rare pic of Me (I'm the cute one in the picture): "Note: I had a wonderful dinner tonight. A certain some..."

So yeah, I know that this is mostly just rambling. It's too early in the morning for much of anything else. Which reminds me -- time to hit the road.

5 Like • Comment • View 9 comments

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