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.

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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.

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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.

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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.

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Turkey DrumStik

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

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September 1, 2019 at 12:46am

#965323

Nineteen

PROMPT September 1st

Celebrate 19 years of Writing.Com by writing a thank you letter to someone on WDC or a thank you letter to the website itself. Then, visit "Writing.Com Party Central 2024!"

(the item will be locked until the wee morning hours of Sept 1st) and tell us what Birthday-related fun you are most excited for.

What do you want me to do, get mushy? I don't do mushy.

But let's give this "thank you" thing a shot.

Dear The StoryMaster

and The StoryMistress

:

19 years, huh? Funny, it only feels like 15. Oh, that's right, I've "only" been here for 15 of those years. Sometimes I still feel like a newbie, but that's because there's so much to do here I still haven't exhausted all the possibilities - a testament to all the good work you've put in to keep things interesting.

19 years is, as you know, a long time in cyberspace. I can't think of too many websites that have been around, without fundamental changes, for longer than that. True, my Amazon account is older, but when I signed my life over to Bezos, it was still "Earth's Biggest Bookstore." The streaming video that sucks away even more of what could be writing time didn't come until later.

A noteworthy accomplishment. But there's more.

See, I've been noodling around on the internet for a long time, way longer than 19 years, and it can be a real shithole. Trolls, scammers, assholes, racists... people who are there to tear you down, pounce on your inadequacies, splatter you with sewage.

But not here. At least not for very long. And that's remarkable.

You've created a community that, for the most part, works. Sure, there's friction - can't avoid that - and it's impossible to please everyone, but you have, for the most part, built a network of relationships based on mutual courtesy and respect.

Because of Writing.Com, I feel like I've grown: as a writer and as a person. More than that, though, I've made friends here - lifetime friends. I've traveled to places I might never have otherwise seen, met people from all over the world both online and in person, had pleasant conversations with people very different from me. This has been my cyberhome for a few days shy of 15 years, and even when I don't write, rare is the day that I don't at least visit, check in, see what's going on.

I'm glad to be here; I'm proud to support the site; I'm honored to be a part of this community.

So.

Simply:

Thank you.

Okay, enough of that.

On to the next part of today's mission. I'll just click on the Party Central link and...

Holy forking shotballs! That's a lot of stuff. Looks like there's something there for everyone.

But one activity stands out for me. See, when I first got here 15 years ago, most of what I stuffed into my port was written for one contest. It's been around longer than I have, obviously, and I have the honor of being involved with it to this day - as a judge, but also sometimes as a contestant as well. In addition to the "contest" aspect, it's just a terrific writing exercise. Yes, of course I am talking about

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So that's what I'm most excited about, if only because I'm a part of it. But I'll be checking out other things as well.

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