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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🌝 HuntersMoon

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa, Snowman Stik

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pon

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

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BIG BAD WOLF is Merry

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

April 23, 2009 at 5:56pm

#646608

Maggie

MAGGIE

1994-2009

One of the reasons I haven't been around much lately is I've been dealing with the declining heath of my cat, Maggie.

She's never been much of a cuddler - with a few notable exceptions - but as her final illness progressed, she wanted nothing more than to sit on my lap as I watched videos. She didn't care much what videos she watched, so I've been going through Star Trek: The Next Generation. I think her favorite character was Data, because he had a cat, too.

These past few weeks, as I knew the end was coming, I've been spending more time with her, letting her sit outside in the sunshine, letting her wander around the yard as she did when she was a kitten. Different yard, same concept.

I got Maggie before my first marriage. My ex-wife thought she was her kitty, so she took Maggie with her. That's when I got Kali and Ghost, to fill the cat-shaped hole in my life. But then I got Maggie back because the ex couldn't deal with her - she was a mischievous little cat when she was younger.

One time, when I had severe neck and arm pain, I was lying in bed, trying not to move. Usually, Maggie would stay on the nightstand while I slept. Like I said, not much of a cuddler. But this time, she climbed up onto my chest and settled down just over the affected shoulder - and started purring, as if trying to make it better.

But Maggie had her dark side - she had a bad habit of not using her litter box, leaving messes in various locations. Not surprisingly, the humans with which I shared a house objected to this, and she was eventually relegated to a comfortable - but lonely - spot in the laundry room. I'd take her out to sit with me when I was on the computer or watching vids or whatever.

And then, as cats do, she started to slow down. She lost weight, and puked a lot. The vet said it was probably lymphoma, but they'd have to do invasive biopsies to be sure. I couldn't agree with cutting open a 14 year old cat just to do biopsies, on the hope that maybe she'd get another six months.

So I waited, and I watched, and I spent every moment I reasonably could with my problem child.

Today, she couldn't walk. And I took her to the vet for the last time. I stroked her and looked into her eyes until the lights went out in them.

Oddly enough, I'd never been there for a pet at the end, before. My old dog died on her own. All my other cats have wandered off, never to be seen again - no closure, just the realization that they're probably never coming back.

This time, there's no "probably" about it. No Schroedinger's Cat here, in any state of quantum - or ordinary - uncertainty; just the end of a crazy calico that no one but me could get close to.

She was a problem kitty, sure - but she was my problem kitty, and until I join her in the great unknown, there will always be someone who has a cat-shaped hole where Maggie should be.

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