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

December 4, 2008 at 3:22pm

#622204

Modest Proposal #3

Last month, I proposed (rather tongue-in-cheekly, or so I thought) repealing Amendment XXII (Presidential term limits), with the implication that we needed to do it now so Obama can take advantage of it in 2016. This was mostly to tweak the ears of the "Palin 2012" crowd. They can make funny jokes; I can make funny jokes.

A few days later, I proposed taxing churches to help with our budget shortfall. I'm actually more serious about this one, though I don't see it happening. And in any case, if it would get churches MORE involved in politics than they already are, forget it.

I'm totally serious about this one:

Legalize marijuana.

Now, I know that most of the people who say that do so from a cloud of sweet-smelling smoke. They see personal benefit in it because then they can have a reliable, safe source for pot, and don't have to freak out every time they hear sirens (in fact, one of the things I like to do to fuck with potheads is to imitate a siren).

Me, I'm not a pothead. Sure, I've smoked it (whoops, there goes my chance at a political career - ha), but it's just not a big deal with me. For me, personally, I could give a shit whether it's legal or not. Unlike with alcohol, which they can pry from my cold, dead fingers, it's not a personal concern.

However, I like to think that my political views go beyond what's good for me, personally, and look at the big picture.

In this case, the big picture includes:

Billions of dollars of taxpayer money spent prosecuting a "war" against a substance that, while not as innocuous as its ardent supporters claim, is demonstrably less hazardous than the legal drugs of alcohol and tobacco and, arguably, less hazardous than many prescription drugs;

Flagrant violations of the fourth amendment through seizure of property of people busted for pot;

Thousands of nonviolent "criminals" clogging up prisons, again on taxpayer bill (granted, some of that is offset by the previous point);

The government missing out on a metric assload of tax revenue.

The people I mentioned earlier, who also support legalizing ganja? They deserve a safe, reliable source of weed. If you're going to ingest a substance, at least let it be as regulated as, say, alcohol.

http://blogs.reuters.com/great-debate/2008/12/03/einstein-insanity-and-the-war-o...

Today's blog entry has been brought to you by the anniversary of Amendment XXI to the U.S. Constitution, which repealed Prohibition 75 years ago tomorrow. So I raise a glass in toast to this great anniversary, but not a bong.

Not yet.

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