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

June 19, 2007 at 5:32pm

#516158

Strip Mining.

I was supposed to be going to a stripper bar tonight.

My friend Ken turns 40 today. I remember turning 40 - it was rough, and I only got past it by committing to start a business; it was either that, or buy a Porsche.

Ken called me last week and said, "What are you doing Tuesday?"

I said, "Working," because that's what I do a lot - see above reference to starting a business.

"Want to take a break? I'm turning 40."

"Aw, man, I'm sorry."

"And I've never been to a strip club, so let's go."

"Um... I've never been, either. But I know someone who has..."

So I called up our mutual friend, Ed. Ed and Ken were the groomsmen at my wedding. To Ed, 40 is a dim, fading memory. "Ed, what are you doing Tuesday night?"

"Nothing." (Ed doesn't own a business.)

"Ken's never been to a strip club, and it's his birthday Tuesday."

"Oh, okay. I have some 'friends' who have been to strip clubs. I'll check with them."

Of course, then I had to bring the subject up with my wife.

"Honey?"

"Yes, dear?"

"I'm going to a strip club with Ken and Ed on Tuesday."

"Have fun."

"You don't want to go?"

"I have a dance thing." (Said dance thing doesn't involve stripping, unless there's something she hasn't been telling me.)

"I won't enjoy it, you know."

"I know." Damn, she knows me.

Thing is, I wouldn't enjoy it. It'd be something I could use as experience, maybe incorporate it into a story sometime, but I don't think I've had a desire to visit a stripper bar since I was, maybe, 16. To me, it's like going to a fancy restaurant, sitting down, reading the menu, watching everyone at the tables around me get served, and leaving after a couple of hours, broke and even hungrier than when I left.

Right now there's people going, "You're comparing women to food! Stop objectifying us!"

No, dear, I'm comparing strippers to food. Strippers encourage the objectification. I've heard strippers say that "I'm going to be objectified anyway, so why not do it on my own terms?" I'm sure that's not a universal attitude; still, if they can call it feminist to do the strip thing, I can call it feminist to refuse to watch them.

Incidentally, while I haven't been to a strip club, there was the bachelor party, which was also arranged by Ed. Probably a little more private than a bar, but it still wasn't my thing - though I appreciate Ed taking the time to set it up for us.

"I looked around and there's just nothing open on a Tuesday, not within driving distance." This was Ed, the next day. I knew the nearest one would be at least an hour and a half away; Charlottesville is too liberal to boast a tittybar.

"Aw, man. Ken's going to be bummed."

But when I called Ken, it turned out he was expecting his brother, who would also be joining us (I don't know him, though). But the brother isn't coming in until Thursday. "Another time, maybe," Ken said.

"Cool." So I don't know - maybe we'll do it another time, maybe not. Now I kind of want to go just so I can say I've been. Instead, Ken and I are going out for beers later. Or maybe beer, singular - his liver's been acting up.

Must be getting old.

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