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 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 7, 2023 at 3:19am

#1060633

No Guaran-Tea

You know what bugs me the most about hotel rooms?

The coffee.

Not really the coffee itself, because I never got a taste for the stuff; I don't like it, so I don't drink it. But it's there, in nearly every hotel room I've ever visited, along with a machine to make it. A machine which might as well be a helicopter for all I know how to use it.

Problem is, I do need my caffeine. Usually, I get it in the form of Coke Zero: way more convenient, because I just have to open a can or bottle. Normally cheaper, too, at least compared to what you get at Starsucks (I imagine it's way cheaper to make the coffee yourself, but I wouldn't know).

But while traveling, hotels tend to charge out the ass for Coke, while the coffee is included in the price of the room.

I'd be okay with that if they also offered free tea. I like tea, especially the darker varieties. Though not Lipton. That stuff is ass. Not even iced tea; just tea bags that could work with hot water from whatever contraption they've cheaply installed in the room.

But they don't.

The one exception I've found is Hampton Inn, which, while I don't think they have tea available in the rooms like they do coffee, usually has bags and a hot water dispenser in the lobby. But then I'm paying more to stay at the Hampton Inn instead of, say, a Super 8, which makes it very expensive tea indeed.

(Sometimes I stay at the Hampton, anyway. It's a solid chain hotel with, usually, a nice breakfast included.)

Right now, I'm on my last night in a Caesar's property in Reno, and the coffee machine is right there on the desk next to where I have to set up the laptop. Taunting me with its complete and utter lack of tea.

Now, I get that this is America and not England, but it's a city with an international airport, so... come ON.

Oh, well, as travel inconveniences go, that's a small one, but I wanted to get this entry in now in case I get stuck in a Donner Pass snowstorm later today.

And won't I be embarrassed if I end up sliding off the mountain to my final doom, and this inane shit ends up being my final written words?

6 Like • Comment • View 4 comments

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