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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Brandiwyn🎶

a day ago
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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 30, 2020 at 12:01am

#999376

December's Eve

Well, I guess this is it for November.

PROMPT November 30th

Congratulations on making it to the last day of the competition! What was your favorite prompt from the last month? What was the most rewarding aspect of participating in the competition?

I gotta say the clear winner, for me, of Favorite Prompt was the Thanksgiving one where we talked about indigenous peoples. Not for my own entry; I kind of strayed off topic, but seeing everyone else's responses was enlightening and illuminating.

I'm actually not irritated about going into December this year, for once. My biggest gripe about December is all the shitty decorations and lame music and faux merriment forced upon us by the Consumer Gods. You know why people get stabby this time of year? It's from having to hear "Simply Having a Wonderful Christmastime" or "Grandma Got Run Over By A Reindeer" on repeat at the stores.

But this year? This year, there is one beautiful, shiny gold nugget in the shitstorm that is 2020, to wit: I don't have to go anywhere. I mean, I usually don't have to go anywhere, but this year it is expected of me to not go anywhere. I can continue to get groceries delivered and other needs met by internet ordering. No dealing with holiday traffic in potential ice storms. No visual assaults by crappy blinking colored lights. No overload of angry red and bloated green. No tacky displays in the shops because I won't be going to any shops. And most importantly of all: no Damnation Army bell-ringalingalingalinging.

Look, I get that a lot of people are actually into that stuff. I'm not asking you to dislike what I dislike. If it makes you happy, great. It makes me grumpy, agitated, depressed, irritated (I know I already used that word) and antisocial. I'm also not ragging on Christmas itself, or any of the other holidays around this time of year; hell, I love the solstice with its promise of renewal and rebirth. It's just the incessant, unyielding hammering of it all, the constant reminder that We Have To Be Merry Or Else! (And Don't Forget To BUY GIFTS!!!)

What I need is cheer in February, not December. February sucks ass.

But like I said, we're all different and while I'm not about to change, I don't expect anyone to agree with me, either. Which brings me to the second part of today's prompt: the most rewarding aspect of this challenge, a thing that keeps me coming back to participate, is finding out what other people like, dislike, and do. Discovering our differences and also illuminating our commonalities.

It's been fun doing that. Stick around -- I hope to have made a blog entry every day this year, and there's only 31 days left to go.

12 Like • Comment • View 14 comments

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