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.

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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 2, 2010 at 8:24pm

#692102

Sitting in my Tin Can

Well, I guess yesterday's April Fool's entry was too over-the-top to be believed, even for a moment. Still, I wanted to do something funny.

The truly great April Fool's joke was perpetrated by Google (a couple years ago, so this is kinda old, but it's not like I have anything else to talk about):

http://www.google.com/virgle/

Seriously, that's an awesome one: For thousands of years, the human race has spread out across the Earth, scaling mountains and plying the oceans, planting crops and building highways, raising skyscrapers and atmospheric CO2 levels, and observing, with tremendous and unflagging enthusiasm, the Biblical injunction to be fruitful and multiply across our world's every last nook, cranny and subdivision...

Sure, it's a hoax, but I figure if it gets people talking and thinking about space exploration again, it's a useful one.

In a story I wrote (and am currently working on editing), which is set about 75 years in the future, I envision an Earth overrun by right-wing extremists; the West by Christians, the Middle East by Muslims, and most everywhere else, some sort of authoritarian society. In this future, we haven't gone much past the moon, and certainly not to Mars.

I know there are people who think space travel's a waste of resources, or that we'd just fuck up other planets the way we're doing this one. I'm not one of those people. Having been raised on a steady diet of science fiction (and science), I know that when we can do something, we will. I don't expect any of the futures predicted by any science fiction writer to come true (and that includes mine); a writer's job is to entertain, and a science fiction writer's job is to envision, not what will be or should be, but what could be.

I also know that human nature will find a way to screw up even the most optimistic of futures. But we gotta try. That's also part of human nature.

"Virgle" is a hoax, but the people involved really are working toward a future of commercially-viable space flight (even if they're not ready to send pioneers to Mars). I say go for it.

And I want my flying car, goddammit!

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