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

December 22, 2009 at 1:00am

#680676

Something about Snow

There's something about snow.

I mean, from one point of view, it's an utter pain in the ass. Like today... okay, actually yesterday, but you know what I mean. I didn't even bother waking up in time to go to work, because there was no way in hell I was getting out. I slept in, giving the sun time to come all the way up (knowing full well that of all the days of the year, it would be "up" for the shortest possible time).

Then I went out and shoveled the bastard stuff. From my front stoop, down the flagstone walk, up and down the sidewalk in both directions, to my truck's doors, and in front of the truck so I could maybe eventually leave. All the time, I was hacking up whatever's been in my lungs as I've been sick on and off all month.

All the people on my street were performing similar activities, with varying degrees of equanimity. My one neighbor (not the hateful bitch uphill, but the nice guy downhill) helped out a bit with the digging out.

It took about three hours.

That is the longest time I've been outdoors since the beach.

My cat, Ghost, kept walking on the fragile film of ice that had formed on top of the two feet of snow. Occasionally, a paw would break through the crust, and he'd shake it and keep walking - until the next paw broke through the crust.

Snow is transformative. I think that's why it's so closely associated with the Christmas season. I mean, in some parts of the US, snow in December may be commonplace, but not here. Here, when we get it at all, it's in January or February, when everyone hates it except for schoolkids. No, snow at Yuletide has the connotation of wiping a slate clean, shaking the Etch-a-Sketch.

I didn't like it, mind you. But it's still transformative. Friday night, everything became quiet, and all I could hear was the soft hiss of snowflakes piling up on the yard (and all I could think was, "Holy shit. I'm going to have to shovel this shit eventually.") Everything became white. Everything developed soft curves, like a supermodel.

I should be writing right now, by the way, and not in the blog. I have a story idea and everything. It's just not flowing. The snow didn't help that.

Perhaps tomorrow.

Anyway, snow. I managed to get out and take my wife to her workplace. I wasn't in any hurry to get to my own - not a lot of work, and it's not like my partner would make it in. Driving around, I was glad I had four wheel drive: bastards hadn't done much to clear the roads. In their defense, this is the most snow we've gotten since forever. In everyone else's defense, what the FUCK are they doing with our tax money?

Three bone-jarring hours later - when snow gets compacted into ice on the road, it develops a nasty washboard effect - I came back home.

I don't know if I'll go out tomorrow or not. I'm definitely waiting for the sun to melt some ice, first.

Still, the snow made things different, for a while.

But not as different as it made Times Square:

http://blog.ricecracker.net/2009/12/20/snowball-fight-times-square/

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