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

March 11, 2008 at 5:02pm

#573031

Recharging

There are, I'm told, people who are recharged in social situations. They become brighter, more confident, and happier when they're in a group.

I'm not one of these people.

I'm recharged by spending time alone. It keeps me from having to wear one of my masks all the damn time.

In the past couple of weeks, while I haven't been posting in here, I've managed to lose a bunch of pounds by exercising and a careful diet, my back pain has diminished to the point where it's almost always bearable, I've started taking pills for my cholesterol problem, and I've gotten back control over some financial planning. At the same time, I've been avoiding people in real life, except for a poker game and what's necessary for work. I had a chance to reset my OWN expectations, rather than living for the expectations of others.

In other words, it's not you; it's me.

The one price I pay is I'm finding myself smoking cigars more often. I know I'm not physically addicted, yet - believe me, I know what nicotine addiction and withdrawal feel like, and there's no way in hell I want to go there ever again - but it's my way of tricking myself into thinking I'm doing something "wrong" in one area so I can let myself be "right" in the areas of physical - and fiscal - fitness.

Life's just not worth living without some sort of vice, and the other traditional ones are fattening, more immediately fatal, or grounds for divorce - or all of the above.

Those of you in Tourn-a-Rounds - sorry for the delay. I expect to post results, and the next round, before the end of the week.

Edited to Add:

By the way, if you would like to reproduce my (so far, temporary) success in weight loss, perhaps this article will help:

http://www.cracked.com/article_15982_5-horrifying-food-additives-youve-probably-...

After that, I wouldn't be surprised if everyone went on a hunger strike.

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