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!

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.

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').

1 Like

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 21, 2019 at 12:02am

#962919

Sweet Emotion

Write an entry inspired by any three WDC emoticons. You pick the emoticons, but make sure they are tied to your entry in some way.

I don't speak emoji.

What I mean is, unless it's, like, a smiley-face or a laughing face, it might as well be a bunch of x's. If someone were to send me a text containing a string of emojis, my mind would simply go blank; I wouldn't even be able to go, "eggplant, poop, alien, waving woman, googly eyes," because my gaze just slides off the string - let alone attempt to translate that into whatever metaphorical language.

Similarly, I don't text people emojis unless it's, like, a laugh, or something equally simple and unambiguous.

Honestly, I miss the early days, when we had to work to make our emotions clear. If we couldn't do so with our words, we'd have to come up with strings of characters to emulate facial expressions. It was a bright, purer time. Kids these days don't know how easy they have it. Get off my lawn.

But I'm used to the WDC emoticons; they're clear and easy to understand.

When I was a baby WDCer, we didn't have as many emoticons. For this entry, I'll pick the three that made me the most excited to finally see as SMs released them during my tenure here.

- believe it or not, the "angel" emoticon had no mirror-universe doppelganger for a long time. I don't remember what year the Devil one came out, but I do remember finally feeling that my life was complete.

I have simple needs.

and all the other donut emoticons - while I eschew the actual pastries (as opposed to chew them) these days for obvious reasons, I was glad to see these appear a couple years back. I use them instead of bullets, especially when giving lists of suggestions in reviews. They don't "mean" anything; they're just tasty, delicious, forbidden donuts. *drool*

But.

is the WDC emoticon I use the most. Also for obvious reasons. So many things elicit that reaction from me, and its absence was a pox upon my existence before it finally showed up in the list.

Now, of course, I can also do this:

But I'm still glad for the emoticon.

1 Like • Comment • View 4 comments

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