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:

🌝 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.

1 Like

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 11, 2008 at 6:38pm

#590368

Artichoke

I bought an artichoke at the grocery store last week.

This was harder than I had anticipated. As I approached the store, the sky turned green and lighting was crackling all around. My goal was to get in, grab some margarita mix, a lime and a few other essentials, and get out.

While I was getting the lime, I saw a few artichokes on display - the biggest, fattest, greenest artichokes I've ever seen. I grabbed the biggest of them; it had a tag around the stem that read, "ORGANIC ARTICHOKE" along with a PLU code. I got the 'choke, the lime, some margarita mix and a few other essentials and got to the self-checkout line.

I started checking out. The PLU code didn't work. There was no option for "artichoke, organic" on the self-checkout screen. I waved at the attendant.

"What's that?" she asked.

"Artichoke."

"Huh. It doesn't look like an artichoke."

It looked like an artichoke to me. I read the PLU code off of the tag for her.

Just then the power blinked, and the self-checkout screens quit working.

I hung around for a bit, but the attendant had run off to do something else and nothing I was doing would work. There was no way the self-checkout would let me check the beer out without the attendant, so I grumblingly picked everything up, put it back in the basket, and went to wait in one of the two 5-deep lines at the regular checkout.

After a half hour of power blinks - at this point, the rain was coming down like Armageddon, so I wasn't going anywhere, anyway - it was finally my turn. The normal registers were working fine, but everyone else had like 60 items, while I had six. I resisted all the candy and such, had a few good chuckles at the stupid-ass tabloids, and when it got to be my turn I whipped out my Kroger card and my credit card.

"What's this?" said the checkout dude.

"Um, it's an artichoke. Has a label on it."

"Oh. It doesn't look like an artichoke."

I squinted; I didn't have my glasses. But it still looked exactly like an artichoke to me. A particularly large specimen, mind you, but... artichoke.

The rain had reduced to a trickle by the time I was done; I went to the liquor store for the rest of the margarita fixins, and went home. The artichoke went into my fridge.

Today, I finally took it out. It still looked like an artichoke, but I could tell that if it waited in the fridge much longer, it would look like a biology experiment, which is more my wife's field. So I trimmed the stem, took off the label, pulled off the most outer bracts, and put it in a half inch of water in a casserole dish and nuked it for five minutes.

When it was done, it still looked like an artichoke, albeit a cooked one. Smelled like one, too. Not the best odor in the world, mind you; they taste a lot better than they smell.

My dad taught me how to eat artichokes. Of course, my mom always overcooked them, like she did everything else, but overcooked artichoke is mostly just more tender. What you do, he explained, is pull off the bracts, dip the base in some sauce (I use a lemon juice, olive oil and pepper mixture; others use more elaborate dressings) and use your teeth to scrape off the tender inner surface. You do this, going around the golden-ratio spiral of the bracts, until you get to where they start to look like the flower petals that they are. Then you pull off the flower petals and scoop out the coarse spines, which reveals the tasty heart. This, too, gets dipped, but you eat it whole.

It's a lot of work. More work, I suppose, than some people think it's worth; I happen to disagree. And I've been to restaurants (The Raven in Virginia Beach, one of my favorite places to go when I'm in that area) where they offer it as an appetizer, with hollandaise sauce. I've seen people at the next table send it back.

"I don't know what this is," they said. "It doesn't look like an artichoke."

People: It's. A. Fucking. Artichoke.

Oh, and look, there's even an artichoke liqueur:

http://en.wikipedia.org/wiki/Cynar

Wow, an alcoholic beverage I haven't heard of. Who says Wikipedia is useless?

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