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.

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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.

July 10, 2019 at 12:01am

#962384

Squirrel!

What’s on your mind right now? Do you have any “brain worms” or current obsessions? If you didn’t have to blog right now, what would you be doing?

I'm sure some people would say that my brain is entirely worms.

But no, I'm mostly just alternating between casually playing video games, finding funny shit on the internet, honing my snark, and watching Season 3 of Stranger Things.

I can't seem to binge-watch like normal people. Even when I was working on catching up on Supernatural or Stargate, I couldn't usually do more than one or two episodes a day. Sometimes, I'd even get squirreled partway through one and shift to snark-honing or game-playing.

In short, my attention span is similar to that of a goldfish, even when it comes to things I nominally enjoy doing.

It's not like this is new for me. No matter what I'm doing, there's always something I'd rather be doing. This was a problem when I had an office job; now, not so much.

Driving helps. It's not like I can split my attention while driving. By taking away the option of doing other things, I get in a focus zone. It's where I do my best thinking, at least if the traffic isn't too crazy.

This is probably why I have several unedited novels languishing on my flash drive (and here). While I can concentrate long enough to come up with short stories or poetry (and, on good days, blog entries), I get to working on the novels and my mind starts to worm around.

Maybe when the next Fallout or Elder Scrolls game comes out (do not speak to me of Fallout 76; as far as I'm concerned, it doesn't exist) I'll go back to being able to do one thing for more than 30 minutes. Not anything productive, mind you, but something.

So, basically, everything is either a) a distraction or b) an obsession. There doesn't seem to be much in between. If this caused me real problems in life, I'd probably try to do something about it. My main focus right now is on weight loss, though, and disturbing my hard-won equilibrium might have a negative (or, I guess, positive, as in the numbers on the scale going up instead of down) effect on that goal.

Fortunately, that's not something I need to concentrate on constantly. I just need to stop myself from ordering pizza or bingeing on Oreos, and in that regard, distractions help.

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