Complex Numbers (Book)

Blog Calendar

◄ April ► 2010
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

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

April 3, 2010 at 10:03pm

#692198

And My Machine, She's a Dud

Actually, today's title is misleading - my pickup truck's working just fine.

For the past couple of years, though, I've been toying with the idea of getting new wheels, though I really haven't done much about it - when I'd first planned on buying, the economy crashed, and I decided I'd hold out a while longer. I've had the truck for 10 years, now.

Besides the lousy economy (which makes it a great time to buy a new car, unless your income has been slashed like tires in the Bronx), the other thing stopping me was:

What the HELL do I want to drive?

Well, apart from this:

http://www.teslamotors.com/

Which I'm not going to get, for various reasons, not the least of which it costs more than I paid for my house.

An SUV or minivan is right out - don't need the space, and don't like the image.

I don't want another pickup truck. I've driven one pretty much from the moment I got my license, I don't really need one anymore, and what's the point of having a mid-life crisis if you're just going to drive the same kind of vehicle?

Sports cars are a big no, too, because they're sports cars and will give people the entirely wrong impression about the size of my man-parts.

And I'm too old for entry-level vehicles.

Plus, I don't really like the cars on the market right now. They all look about the same, and the ones that don't, well, they look ugly.

And I'm painfully aware that, for the first time in my life, I'm actually considering "image" as one criterion in car selection. Which is why I'm avoiding BMWs and Mercedeseses. Or anything from Detroit.

So I have to ask myself: "What kind of car can a middle-aged guy drive without making it look like he's reliving a lost childhood or looking forward to retirement?" (This is especially hard to answer because I want to relive a lost childhood and I'm looking forward to retirement.)

And there's just not much out there like that. Everything's geared toward college kids, families, or bald guys with Issues.

I test-drove a Subaru and a couple of Nissans today. Not bad, but I didn't exactly fall head over heels for either make. And the Toyota dealership completely ignored me. Yep - guy walks in on a slow day at a time when Toyota's reputation is in the toilet, and they wouldn't even talk to me. Maybe it was the Bruce Springsteen tour shirt I was wearing, but that didn't slow down the Nissan folks.

Fortunately, I'm in no hurry. But it bugs me that I can't even decide on a freaking CAR.

Comment • View 6 comments

© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.