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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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

Nov 14, 2024 at 12:10pm
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').

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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

January 24, 2019 at 12:56am

#950325

On Writing

How did you start writing? Did someone urge you to write, or did it come naturally?

I started reading at an early age.

Before public school, even before kindergarten (which, at the time, was not part of the public school system), my parents taught me to read.

I don't remember much of those early lessons. I think they involved deciphering cuneiform scratchings on stone as we ran from the saber-toothed tigers that were chasing us away from the woolly mammoth kill. Or maybe I'm misremembering.

Consequently, I always read above my grade level. This would cause me problems later in life, as I read things like Stranger in a Strange Land when I was still quite young, and it warped me.

But that and other writings - mostly, but not all, science fiction - led me to believe, in the way young people believe without evidence or accountability, that I could do that too.

So, I tried. As with most people, I think those early efforts would embarrass me now, but I do remember my parents and teachers encouraging me.

Because I was good at nerdy stuff, I sucked at sports, so I wrote.

Because I was never skilled at any sort of graphic arts, I wrote.

Because we weren't wealthy, I was happy to be able to create something with no raw materials besides a notebook and a pencil.

I learned words. I lived and breathed words. When I wasn't writing, I did crossword puzzles to improve my vocabulary. I paid attention in English classes and learned (with varying degrees of success) the rules of spelling, grammar, and punctuation.

Thing is, I was also pretty good at math, and to be honest, math pays better, so I went into a field that was more math than writing. There was some need for technical communication in engineering, though, so I learned that as well, and creative writing faded into the background.

But it never completely disappeared, as you can probably tell. With my background in science fiction combined with my engineering training, I could still craft a story when I put my mind to it.

I'm still learning, though. Sometimes it's hard to know when to be less technical and more poetic. And my sense of humor usually creeps in, sometimes inappropriately. And I'm a long way from mastering the intricacies of plot and characterization, but I'm still working on improving.

I write because there's almost nothing else I'm any good at.

6 Like • Comment • View 4 comments

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