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

October 28, 2008 at 6:41pm

#615275

Freedom, Continued

I've been hearing a lot more complaints about "redistribution of wealth." Some people seem to think that the moment Obama gets elected next week, we're going to have to begin handing over our paychecks to the government, who will immediately turn around and give it to a Mexican immigrant in New Jersey.

That's obvious bullshit. Intelligent people know that we're going to have to begin handing over our paychecks to the government, who will immediately turn around and give it to a foundering bank in Delaware.

But seriously, folks... what the hell? You think the President has that much power? I'm sure Barack would be flattered to hear that he'll be able to do such a thing.

Okay, I doubt too many hard-core right-wingers read this blog, but if you do, and you seriously have a problem with wealth redistribution for perceived public good, I want you to immediately do the following:

1) If you're currently taking an exemption on your Federal income taxes because you have a child or children, stop immediately, and never take such an exemption again. If not, when you do have kids, don't claim this exemption.

2) If you have EVER taken such an exemption on your Federal income taxes, immediately refund the Federal government the amount of all those exemptions.

3) Begin to lobby for the elimination of the child exemption on Federal income taxes, as it unfairly transfers wealth by causing those who do not choose to have children to pay more in taxes than those who do not and, in fact, causes those who use fewer government services to pay more.

4) Begin to work on the local and state level to ensure that schools are paid for entirely by people who are currently using them, or their parents, because the people who are not using the education system should not have to pay for something that does not directly benefit them. (Exception: lottery proceeds may continue go to education, as this constitutes a voluntary tax.)

If you hold such beliefs, yet can't or won't do all these things, then you are admitting that there are, indeed, cases where wealth can be redistributed for a perceived public good, and we can go back to arguing about what cases truly constitute "public good."

For my part, I don't mind paying for other peoples' kids' education, because I recognize that an educated populace is something that benefits everybody, directly or indirectly.

Look, everyone (well, "my fellow Americans" anyway), the US government is in DEEP debt. Will our taxes increase? Yes, they probably will, no matter who gets elected next week. But will those taxes go to helping the poor or propping up those who have lost their jobs? No, so you can put your fears of "socialism" to rest. The tax increase will go to paying off the inconceivable amount of debt that we've amassed, but we don't feel because a certain administration has taken the "tax" part out of the "tax and spend" equation.

The bill's coming due, and you're all [right-wing nutjobs] bitching because one of the candidates has a proposal to slightly increase - slightly - the incremental tax on people making more in a year than I can pull down in THREE years? A plan that can't even be implemented unless Congress goes along with it, which never happens even when it's all run by the same party?

Put up or shut up.

Note: In case it's not perfectly clear, I'm not addressing this rant to the perfectly reasonable people who are fiscal conservatives. I'm one myself, though you can consider me a social liberal. Just the right-wingers who aren't making any FUCKING SENSE.

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