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 4, 2007 at 6:51pm

#546778

Blast from the Past

I met my friend Pat when I was in 8th grade and he was in 7th. As I recall, we both had it for the same girl: Karen. I think he actually succeeded in hanging out with her more than I did, the bastard.

In high school, though we were in different grades, we were always doing the same stuff, and once I got a car I'd give him rides to school. After he graduated, we took a couple weeks and went to Florida the long way. There's a picture of us, I think from Jacksonville, and damn we look young. I'm going to see if I can find it again and scan it in.

Pat ended up pursuing a journalism career; I went into engineering. For a while we lived in the same house when he had a job with a local paper, and then he left. We kept in sporadic touch. He married an older woman with a kid, and so became stepdad to a teenager. I never had kids. He moved around the country, from Missouri to Florida to Arkansas; I stayed in one place. He's one of the few people, and the only guy, from my school days that I've managed to keep in touch with, and that's mostly through his efforts.

But now Pat got a job with the Charlottesville newspaper, and he's on his way back here for the foreseeable future.

He and I are different - he's a conservative; I lean liberal, though I tend to be conservative in economic matters. He has a kid of his own now. But we've known each other for a long time, and we both drink - and that has to count for something.

Comment • View 3 comments

November 4, 2007 at 5:40pm

#546762

B minus 7 Days

1985: The one that got away

Having had such an awesome time at the 1984 show, I decided when Bruce came back to the DC area the following year, I had to try for tickets.

Remember, this was pre-Internet, so in order to get tickets you had to call them, hope you got through, and then deal with credit card nonsense.

Never did get through. Show sold out in less than a half hour.

I checked the Washington paper for a few days after that, and people were selling front row seats for over $2500. Now, I'd pay that for Bruce tickets... but in 1985, I don't think I had 1% of that in my bank account.

It turned out the concert was the night before a summer school math exam anyway, and it was probably best I didn't go so I could pass the class. But I would have.

We busted out of class had to get away from those fools
We learned more from a three minute record than we ever learned in school
Tonight I hear the neighborhood drummer sound
I can feel my heart begin to pound
You say you're tired and you just want to close your eyes and follow your dreams down

We made a promise we swore we'd always remember
No retreat no surrender
Like soldiers in the winter's night with a vow to defend
No retreat no surrender

Comment

© 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.