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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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 20, 2007 at 9:52pm

#550533

A Moment of Shining Light

Okay, remember how my last entry was all about hating everything for the next month or so?

I might have to cancel that this year.

Why, you ask? When you were SO looking forward to another 31 days of grumpy bitching, pissing and moaning?

It's simple.

Bruce Springsteen extended his tour dates into 2008.

That's not all.

On the evening of April 30, 2008, the band will perform in my town!

I'm calm. I'm calm.

Now all I have to do is get tickets... I managed before; I can do it again. They haven't announced the sale date yet.

Hallelujah! Praise be, brothers and sisters! Testify, my friends! The Light is upon me!

The only thing that could possibly make this better would be backstage passes. I'm sure the local stations will be running promos. I'll be doing a lot of radio listening over the next few months.

Amen!

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November 20, 2007 at 12:27pm

#550399

Offensive

I've been getting some flack lately for some of the things I've said. They've been insensitive, callous - even offensive. My wife took me to task for being bitter and cynical. I told her that it's only going to get worse as the "holidays" approach, especially if I'm lured out of my cage to go to stores. Why, just yesterday, the red and green decorations at the grocery store made me contemplate reindeericide.

All the fake cheer, all the ringing bells, all the extra traffic, all the long lines, all the sappy, crappy Santas and bright penguins and laser-nosed reindeer - all this conspire to overshadow even my arch-nemesis Hello Kitty as the bane of my existence for one month out of the year.

So yeah, it makes me cranky, and when I get cranky, I rag on things. I don't set out to offend, but it happens. If it helps - and it probably doesn't - everything's fair game when I get on one of my holiday jags. If you don't like it, I suggest skipping this blog until after the solstice, at which point I usually start to feel better.

But just to show that I'm an equal opportunity offender, I present these gems, collected from the Internet. Of course, I don't find these funny at all; in fact, they offend me terribly. *snicker*

Q. What should you do if you see your ex-husband rolling around in pain on the ground?
A. Shoot him again.

Q. Why do little boys whine?
A. Because they're practicing to be men.

Q. How many men does it take to screw in a light bulb?
A. One - he just holds it up there and waits for the world to revolve around him. Or, Three - one to screw in the bulb, and two to listen to him brag about the screwing part.

Q. What do you call a handcuffed man?
A. Trustworthy.

Q. What does it mean when a man is in your bed gasping for breath and calling your name?
A. You didn't hold the pillow down long enough.

Q. Why does it take 100,000,000 sperm to fertilize one egg?
A. Because not one will stop and ask directions.

Q. Why do female black widow spiders kill their males after mating?
A. To stop the snoring before it starts.

Q: Why do men whistle when they're sitting on the toilet?
A: Because it helps them remember which end they need to wipe.

Q: What is the difference between men and women?
A: A woman wants one man to satisfy her every need. A man wants every woman to satisfy his one need.

Q: How does a man keep his youth?
A: By giving her money, furs and diamonds.

Q: How do you keep your husband from reading your e-mail?
A: Rename the mail folder to "instruction manuals"

Now, back to my regularly scheduled grumbling.

Comment • View 6 comments

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