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.

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

January 20, 2007 at 9:08pm

#482605

Furniture

I was hoping to stay home today. As you know, that's my preferred mode of existence, anyway. I've been known to get sunburns walking from the door to the car. But my wife had other plans.

Oh, I'm not resentful or anything. In fact, I figured we'd do it as early as possible so I'd have time to do my Daily Writing Challenge (increasing to 1900 words today) and a blog entry and some reviews I'd promised a while back and a whole bunch of other stuff, not excluding some time to play Oblivion.

The first step was to remove Kirstin's old dresser, a long, low number with nine drawers. We took the drawers out - okay, she took the drawers out and we emerged, me blinking and squinting in the unaccustomed sunlight, to tilt the bloody damn thing into the bed of my pickup.

To the Salvation Army we went - sadly. I despise the Salvation Army, not least because I can't go to the grocery store between Halloween and Christmas without hearing, "ding ding ding ding ding ding..." But the Goodwill around here doesn't take furniture, and there was no way I was going to pay to take it to the ducking fump. So to the Army we went, me squealing tires so I wouldn't have to hear them ask God to bless me.

Then it's up to the furniture place to get Kirstin's new piece of furniture, a much narrower and taller thing that fit better in her room. Yes, we have separate rooms - though all she uses hers for is keeping her clothing and various bellydance supplies. One of the advantages of not having kids - our modest four-bedroom house has exactly one room to sleep in. Anyway, I'm in the driver's seat when the thing gets dumped into the bed, and I swear my front wheels come up off the ground for a moment as it bounces in.

On the way back, I'm having fun hoping the brakes continue to work - what is it about a sunny Saturday afternoon that brings out a load of crazy drivers, anyway? When we finally get home, we try to take the bloody thing out of the truck.

It's not budging.

I go get the handtruck, and together, we manage to tilt the thing up on its side, maneuver it over the tailgate (fortunately, the truck is parked facing uphill, else that would have been impossible), and onto the dolly. Then we wrap bungee cords around the thing to secure it to the dolly. These turn out to be useless, since even though we'd stretched them to the limits of our strength, as soon as I tilted the hand truck backwards, they stretched even more.

Still, we managed to get the assembly tilted onto one corner, maneuvered it up over the curb, up the lawn (yes, uphill), past two steps onto the front stoop, and over the threshold.

It's the foyer stairs that become our nemesis.

We live in a split-foyer house, and it's all we can do to lift the dolly up over the lip of the lowermost step. Then it's wait to catch my breath, and we manage to get it up over the next step, though I end up overextending my elbow. Ow.

And that's it. It's not budging. That's when I finally look at the weight stamped on the side of the carton:

90.6 kg.

That's, like, 200 pounds. And that's not counting the hand truck, or the force necessary to have the hand truck's wheels clear the stair lips.

So we do what any couple with severe, chronic back issues would do: We call my brother-in-law, who fortunately is no more than five minutes away. Meanwhile, I'm upstairs, and my wife is in the foyer trying to keep the thing from slipping backwards. Just for fun, I let go of it and go get something to drink. "Mmmm, that's good!" I exclaim, downing some fresh, icy water. "Damn, I needed that drink!"

Remember, all of this is HER fault. Yeah.

Anyway, finally her brother arrives, and we manage to get the bloody damn beast up the rest of the stairs, out of its carton, and into her room, without dinging up the walls. Go us. The thing has more drawers than Victoria's Secret, by the way. Dozens of the little buggers.

So now I'm sitting here with my back in spasms and my elbow all swollen, causing me pain every time I hit the keyboard. So why am I telling you this on top of the 1900 words I've already written?

Beats me.

Tomorrow, her mother is taking us all out to the local fancy steak house (Aberdeen Barn), so at least I get a free meal out of her family for all this. But until it's time to get dressed and go out, hopefully after sunset, I'm going to sit in the house. Playing my video game. In my underwear.

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