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 12, 2007 at 4:57pm

#480888

Thumpers in the News

http://seattlepi.nwsource.com/local/299253_inconvenient11.html

This week in Federal Way schools, it got a lot more inconvenient to show one of the top-grossing documentaries in U.S. history, the global-warming alert "An Inconvenient Truth."

I'm not going to comment on the validity, or lack thereof of the documentary. However,

After a parent who supports the teaching of creationism and opposes sex education complained about the film, the Federal Way School Board on Tuesday placed what it labeled a moratorium on showing the film.

"A" parent? As in, ONE? One person complains, and you pull the film?

"Condoms don't belong in school, and neither does Al Gore. He's not a schoolteacher," said Frosty Hardison, a parent of seven who also said that he believes the Earth is 14,000 years old.

Attempting to discredit a source by putting in his beliefs about the Earth's age is unworthy journalism. After all, he lost credibility with me from the get-go.

"The information that's being presented is a very cockeyed view of what the truth is. ... The Bible says that in the end times everything will burn up, but that perspective isn't in the DVD."

Okay, so the Bible belongs in school, but not Al Gore?

This is about when the

went off in my brain. I finally figured out why the Religious Right opposes the idea of global warming. See, at first I thought it was because they, the Republicans, and Big Business are all in bed together, and since Big Business wants to turn a blind eye to the possibility of climate change (it would cost them money), the others follow along. Then I figured it was because the Right Wingnuts read in that there Book that we have "dominion" over the Earth and all that crawls upon it, or however it's worded - which is patent nonsense, regardless of its source. My last theory was that they simply didn't give a shit because the Rapture's right around the corner, anyway, so why fret about using up the world?

But no, those reasons may enter into it, but now I understand the basic, fundamental (ha) reason the thumpers ignore anyone who says global warming is occurring:

It would mean that a substantial part of the world will be destroyed in a flood.

And God promised us that the world would never be flooded again.

So you see? Logic: God promised not to flood us out, and global warming would result in a flood; therefore, global warming must not be happening.

Lord, save me from Your followers.

School Board members adopted a three-point policy that says teachers who want to show the movie must ensure that a "credible, legitimate opposing view will be presented,"

This is the part that pissed me off the most. The damn thing was pulled because some superstitious, anti-intellectual Bible-thumper didn't like the conclusions it reached - a thumper who, moreover, thinks the world is only 14,000 years old! Now, he may have an opposing view, but there is no way in hell it is either credible OR legitimate - as science. It may be credible as religion, but then we'd be teaching religious doctrine in schools!

Please note I'm not saying I "believe in" global warming, here. I'm not qualified to say whether it's happening or not. Neither, I'd wager, is anyone on the school board in question, and certainly not the thumper who bitched.

Speaking of bitching thumpers, this one comes not from here but our neighbors to the north. Blame Canada!:

http://www.cbc.ca/canada/british-columbia/story/2007/01/09/bc-yoga.html?ref=rss

A school program to fight childhood obesity that includes yoga is drawing complaints from some Christian parents in the Quesnel area in B.C.'s Cariboo region.

They say yoga is a religion, and shouldn't be taught in public schools.

Okay, I'm not familiar with Canada's version of the separation of church and state, so I don't know if this has any legal force or not.

However, consider this: in the US, thumpers have been trying to insinuate religion into schools forever. The "under God" part of the Pledge, "moments of silence" for prayers, and so on. And I have heard that studies have shown that prayer has many positive effects on a person. Blood pressure, I believe, was cited, along with other general benefits.

But get this:

It doesn't matter TO WHOM you pray. You get the benefits anyway. And like some wag once said, as long as there are math tests, you're going to get prayer in schools.

While yoga certainly has its roots in religion, it's grown beyond that into something practiced secularly for general well-being. If we were to ban everything with its roots in religion from schools, we'd have to disallow the calendrical system - come up with some other way of counting years. Okay, that's a bit extreme for an example, but doesn't it make a difference HOW the yoga is presented? As well-being, or as a specific spiritual path?

"There's God and there's the devil, and the devil's not a gentleman. If you give him any kind of an opening, he will take that."

I say again: Lord, save me from Your followers.

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