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

January 13, 2009 at 3:57pm

#629469

Pursuit of Happiness

I like science. Science is good. Science leads to a rational worldview and technological advances, and a better understanding of the universe.

However, things like this make me want to kick something.

10 Things Science Says Will Make You Happy

http://www.alternet.org/healthwellness/111138/10_things_science_says_will_make_y...

1. Savor Everyday Moments
Pause now and then to smell a rose or watch children at play...

Look, the last time I stopped to smell a rose, a bee came out and stung me on my damn nose. And the last time I was watching children at play, a couple of big, beefy cops came up and took me away. Now I'm on a List.

2. Avoid Comparisons
...Instead of comparing ourselves to others, focusing on our own personal achievement leads to greater satisfaction...

My personal achievement needs to include doing better than the Joneses.

3. Put Money Low on the List
...“The more we seek satisfactions in material goods, the less we find them there...”

I don't want material goods. I just want money. Enough money so I don't have to work anymore. Keep the "material goods." Just give me money.

4. Have Meaningful Goals
“As humans, we actually require a sense of meaning to thrive.”

My goal is to have money. That's meaningful.

5. Take Initiative at Work
...when we express creativity, help others, suggest improvements, or do additional tasks on the job, we make our work more rewarding...

BFPPPHHHAHAHAHAHA! When you do all THAT shit at work, most places, they'll either fire you or look at you like you're weird.

6. Make Friends, Treasure Family
Happier people tend to have good families, friends, and supportive relationships

Whereas everyone I know has a dysfunctional family, and talking about it makes them happy (see this week's Comedy newsletter for more details).

7. Smile Even When You Don’t Feel Like It
...Even if you weren’t born looking at the glass as half-full, with practice, a positive outlook can become a habit.

I'm positive. I'm positive this article is a crock of horsepuckey.

8. Say Thank You Like You Mean It
...people who write “gratitude letters” to someone who made a difference in their lives score higher on happiness, and lower on depression...

I want to thank you all for reading my blog. It really makes a difference to me. There - I'm going to be positively GLOWING for the next month.

9. Get Out and Exercise
...regular exercise offers a sense of accomplishment and opportunity for social interaction, releases feel-good endorphins, and boosts self-esteem.

The last time I went to the gym, there in the locker room was the elderly judge who presides over the Federal Grand Jury on which I've been serving for most of a year now. He was completely starkers, bent over and toweling off his leg. I will never, ever be able to get that image out of my mind, even with a 55-gallon drum of eyebleach. If this is what regular exercise has to offer, you can freaking KEEP it.

10. Give It Away, Give It Away Now!
...you get more health benefits than you would from exercise or quitting smoking...

Oh good; that means I don't have to exercise or quit smoking. Provided I don't have to see any naked judges, that's Just Fine With Me. Oh, and that song you quoted? One of the stupidest ever.

This list sucks. I need a Cracked list as an antidote.

Here:

6 Obnoxious Old People Habits (Explained by Science)

See? We're still talking about science here, but this one's going to be GREAT.

http://www.cracked.com/article_16952_6-obnoxious-old-people-habits-explained-by-...

How many times have you gotten behind some large sedan going 30 mph on the highway, only to notice it's being driven by someone born during the Great Depression? Do you stop to say, "One day, that'll be me!"

Because it will.

Now I'm happy.

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