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

October 27, 2009 at 5:52pm

#673527

Backwards

I fully admit that it's backwards, but it's the way I am, and I have to accept that, even if my friends and family don't understand - which they don't.

See, when it comes to music, as you've already figured out, I'm not normal. First of all, I don't either love or hate a song. For most people, it's like Beavis and Butthead: either it's cool, or it sucks. But as they once said, "If everything was cool, and nothing sucked, how would we know what was cool?" For me, there's a whole spectrum from "suck" to "cool." About some songs, I'm just indifferent.

Second... well, what's "cool" for me has a wide range of styles, including what some would call "depressing" songs and what some would call "happy" songs. I like 'em both - when they're done right. The thing is, "depressing" songs make me smile. They make me happy. I don't know if it's because of my finely-honed sense of schadenfreude, or because I just like a good sad song, or because I can say my situation is superior to that described in the song.

Meanwhile, "happy" songs make me want to cry. (I don't actually cry, of course; I'm a man, after all.) They show me a glimpse into a world from which I am forever barred from participating. It's not that my life sucks; it's just that joy has been elusive to me. I get a small taste of emotion from these songs, but I try not to overdo it.

So today's video is a song about what most would consider a depressing subject, but it's one that never fails to make me happy. It's from The Boomtown Rats, who were probably better known for their lovely, upbeat song about school shootings, "I Don't Like Mondays." I love that song, too, but for whatever reason, the one I link here is the one that sticks in my head as an all-time favorite. From the depths of 1979, I present:

(the Rats gave us Bob Geldof, who is now better known as the organizer of Band Aid and Live Aid, but I will always remember as the main character in the movie Pink Floyd: The Wall.)

Oh, and here's a more recent picture of Bob Geldof - ah, the ravages of time. http://prod.campuscruiser.com/news/22/1188826/91682/Bob+Geldof-w275-h344.JPG

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