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.

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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.

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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.

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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.

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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.

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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"

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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!

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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.

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May 1, 2010 at 11:43pm

#694918

One pill makes you larger

I've never really come out and said this, but it should be obvious from some of my entries that I'm prone to depression.

Some time ago, before I joined WDC, I tried a prescription for antidepressants that my doctor recommended. That didn't last long. It lasted, more to the point, for about a week, until one night I found myself floating above my bed and looking down at myself lying there. Sure, it was a dream or hallucination - I don't levitate - but that's just one of those things that we're not supposed to experience or, if we do, we should be under the influence of something more recreational than Paxil.

Not that I do recreational drugs, mind you (well, I drink, but nothing illegal. That would be the LAST thing I need, getting a dependency on something like that.)

I lived with it - the depression, not the medication - for a while, rationalizing it by thinking that some of the best writers have suffered from depression, and I might as well get what creativity I could out of it.

The problem is, I don't get very creative when depressed; instead, I find myself starting to write angsty poems which I immediately delete (teens, take note: write them all you want, but freaking DELETE them before inflicting them upon the rest of us. You're not Poe. You're not even Morrissey.)

More recently, I've found that a combination of two things clears the depression right up: exercise, and vitamin D. Either one alone helps, but together they make me positively cheery, at which point none of my friends want to be around me because they're used to me being cynical and apathetic. That bums me out, which makes me depressed even when I'm not. Maybe I need new friends.

Well, I haven't been exercising very much over the past month - no excuse for that, just haven't worked it into my schedule, but I've been taking the vitamins.

Last night I forgot to take it, so today I found myself driving down the back roads of rural Virginia listening to Leonard Cohen and Brandi Carlile - not something I recommend in megadoses for one's mental health.

What really bugs me about all this is that it's all chemical - either directly as in the vitamin D, or indirectly through production of endorphins via exercise. In other words, no event can "cheer me up" for any length of time.

I don't know WHY it bugs me that this is the case; it just does.

So tonight I'll remember to take the vitamin D, and tomorrow I'll go to the gym. And maybe I can save a bit on gas in the process.

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