Complex Numbers (Book)

Blog Calendar

◄ November ► 2007
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

November 5, 2007 at 5:22pm

#547087

B minus 6 Days

1988: The Day The Music Died.

Yeah, I know the Music died on February 3, 1959. But for me (which is all that matters), it died on some unremembered day in late 1988.

I was living in a two-bedroom basement not far from where I live now. Pat had moved out, and I'd been unable to find a replacement roommate, so money was tight. My stereo and LP collection (I was still resisting the purchase of CDs, as I lacked a CD player) was in the living room closet, as I was using that space for nothing else and music has always been of paramount importance to me.

My LP collection at that point was over 150 records, including rarities, and super-rarities such as an original pressing of Billy Joel's Cold Spring Harbor. Plus I had my entire collection of singles on 45 rpm discs (who remembers those? They were fun.)

On that fateful day, I opened the door to my apartment and stepped into a foot of water.

The stereo itself survived, being raised off the floor by its case.

The records were destroyed.

Water doesn't destroy records all by itself, of course. But it soaked the album covers, resulting in paper pulp and glue attaching itself to the bottom chord of the records.

I still haven't thrown them away; I simply can't bring myself to do that. They're sitting in a box in the attic of my father's house. It took me until The Rising came out to replace my entire Springsteen collection with CDs; I still haven't replaced some of them, such as Styx's Cornerstone and Pink Floyd's Dark Side of the Moon (which, as much as I revere Springsteen's entire output, remains my favorite album of all time, and just doesn't sound the same on CD).

I didn't do much listening to music from that point on. It just wasn't the same anymore. I'd been disillusioned; what I thought was forever was gone in a day. Could that incident have influenced my later career, which is focused on drainage and hydrology? Possibly. But I may not have learned my lesson; my entire comics collection is stored in our basement. Still, losing the comics would be sad, but it wouldn't come anywhere near the tragedy of the Day the Music Died.

I had a job, I had a girl
I had something going mister in this world
I got laid off down at the lumber yard
Our love went bad, times got hard
Now I work down at the carwash
Where all it ever does is rain
Don't you feel like you're a rider on a downbound train

Comment • View 1 comment

November 5, 2007 at 1:02pm

#546997

A Kindred Soul

At last, I have found a place on the Internet where I truly belong - besides Writing.com, that is.

And I thought I was all alone until I found:

http://www.kittyhell.com/

On a less positive note, I thought I'd seen everything until I ran across this. Oh, the humanity! Thank you, Paris, for raping my childhood.

http://www.cameltap.com/?p=981

Comment • View 5 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.