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 19, 2007 at 1:59pm

#482387

Commentary

Okay, folks, no squicky or gross links today, I promise. Though the links I do provide might make you angry.

I thought I'd take a few moments to address some of the comments from yesterday's controversial entry:

darkin: You know, Robert, I could have gone my entire life without reading that first article! MY ENTIRE LIFE!!!!

Well, darkin, I know how much you care about others, and you wouldn't have wanted me to suffer the misery of reading that article all by myself, would you? You were just being your usual altruistic, unselfish self. I'll be glad to continue to help you help others

Kenzie

: Yikes. I think you've managed to make this optimistic person think unkindly about mankind. That's not an easy task.

My work here is done.

Nada

: Turning green here....gawd, thanks soooo much for sharing. I don't think I could have even put that into my Sunday Funnies it was so gross. If you promise not to share that kind of stuff I'll come back.

I promise not to share that kind of stuff... today. Realistically, probably not again for a while. I tend to think this was a one of a kind sort of experience

dragonfly~guess who's back?

: Wow--that was pretty icky. kudos to you, sir, for providing us all with our icky qouta for the week.

I have to add, that as I've read more of the previous blog entries, you have gained a new reader!

Translation: "I'd love to see this sort of thing about once a week, and your other blog entries have been much, much better."

Seriously, thanks for reading!

elusive ennui warm inside

: yes... well did they ever ask if he'd eaten any of it? never eat anything the cook wouldn't eat...

And never eat anything with the word "Surprise" in the name.

Mavis Moog

The meatball thing is art. It's challenging a deep seated modern taboo.

I'm all for challenging taboos; just look at some of my writing. It's useful to me to consider three levels of action: thought, word and deed. When considering a taboo action, the first thing that happens is thought - even if, as occurs in some crimes of passion, that thought is short-lived. One of the great eye-opening moments of my life came when I finally realized that there are people - nay, entire religions full of people - who seem to take the thought as the deed. That is, some consider that to even think about, say, adultery is the same thing as doing it. This honestly never occurred to me, and I strongly suspect it is just another example of organized religion keeping people in line by making them believe they're Bad - because who can control their initial thoughts? If I convince you that purple elephants, for example, are unclean and that any association with purple elephants will condemn your soul to eternal torment, well, oops, too late, you've already imagined a purple elephant, haven't you? You're going to Hell unless you give me 10% of your pre-tax income from now on. I take PayPal.

ANYway, the point is that I am convinced that there is no harm in harboring thoughts involving taboo actions. There may be some implied harm when the thoughts go to the level of words - either spoken or written - depending on the context. For example, if someone says "I think pot should be legal," it's not the same thing as saying "I smoke pot." Further, the one does not imply the other, though the latter expression may lead impressionable people to break the law, to their detriment. The final level, deed, is where the real trouble comes in. Deeds have real effects on other people. Some of you may recall my distinction between reality and imagination: imagination affects only you; reality affects other people also.

That said, I will continue to challenge taboos in my writing. I'm still not eating meatballs.

Speaking of taboos, let's look for a moment at one taboo that really isn't, much, anymore, except, apparently, in North Dakota:

http://tinyurl.com/25z5uk

North Dakota is one of the few states that outlaws cohabitation, which is defined as a man and woman living together "openly and notoriously" as if they were married... It is listed as a sex crime in state law, alongside adultery and incest.

Okay, let me get this straight... You're a guy living in North Dakota with his girlfriend. They catch you and try you, and you're convicted of cohabitation. You get sent to jail for a month and get fined $1000. Okay, no biggie, lots of people have spent a month in jail and had to pay $1000 fines. But now you have to register as a sex offender, and for the rest of your life you have to have your name pop up on registries, never be able to adopt, live in restricted communities amongst real sex offenders like child molesters and rapists? What the fuck is wrong with people??!

"If we look at the research, social science evidence suggests that living together is not a good way to prepare for marriage, or to avoid divorce," Freier said. "Cohabitating is not positive for the family, and poses a special risk for women and children."

You mean like this happy family, here?:

http://tinyurl.com/34gq9m

Tigger thinks of Prancer

: Anyway, I think I'm going to bring meatless balls to work for lunch today.

*covers self* Damn, Tigs, I knew you were a feminist; I just didn't know you were THAT militant!

novusfemina: As for a Robot that builds houses.. why didn't they make a robot that CLEANS houses first?

Because they're still working on getting the boobs to look realistic. Snoogans!

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