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.

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.

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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.

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!

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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.

3 Like

April 17, 2007 at 5:33pm

#502339

Meat Loaf

Last night was the rescheduled Meat Loaf concert. My wife wasn't interested in schlepping all the way back up to DC, so I ended up going with one of my employees, a guy quite a bit younger than I am who also happens to like Meat Loaf's music (otherwise, he wouldn't have been able to last this long here).

All I can say is, the dude can still rock.

I'd been warned that he might not play very long, having been ill recently. The concert was supposed to start at 8, and the band took the stage around 8:25 - not bad as these things go. The first set was all older tunes, classics such as Paradise by the Dashboard Light, which was perfomed with this skinny brunette chick who could sing.

Not that Meat Loaf couldn't. His voice was a bit rough in places, as he'd been sick, but he belted them right out. The band was tight (not just the brunette

), and I think carried him over some tough spots.

After a short break, they played the studio version of "I'm Still Alive" (from new album) over the speakers while showing a montage of scenes from movies Meat Loaf has been in, including two of my all-time favorites: Rocky Horror and Fight Club.

Then the band pounded into the second set, mostly stuff off the latest album, though it also included a powerful rendition of "Two Out Of Three Ain't Bad" - admittedly, not my favorite song, but done well.

The biggest surprise for me, though, came after they played "Bat Out Of Hell" - they came back for an encore, as is usual, but the encore consisted of some rockin' covers, including Rolling Stones' "Gimme Shelter."

As the show ended, Meat Loaf finished by bellowing out, "Don't you ever stop rockin!"

Say what you want about Meat Loaf; the dude can put on a SHOW. It was totally worth the money and the wasted trip up there, as well as the return trip in the cold, windy rain. Sometimes he looked his age. Other times, he projected the energy that made him a tour sensation in the 70s.

But mostly, I came away from the concert feeling good about myself (which is what concerts are supposed to be about, yes?) - because in watching the performance, it finally hit home to me that you don't have to be beautiful to be appreciated, and you don't have to be slender to be loved.

And I'll never stop rockin'.

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